Theorem: Groth16TypeI.is_sound
Proof state before:
case intro.intro.intro
F : Type
inst✝ : Field F
n_stmt n_wit n_var : ℕ
u_stmt : Fin n_stmt → Polynomial F
u_wit : Fin n_wit → Polynomial F
v_stmt : Fin n_stmt → Polynomial F
v_wit : Fin n_wit → Polynomial F
w_stmt : Fin n_stmt → Polynomial F
w_wit : Fin n_wit → Polynomial F
r : Fin n_wit → F
stmt : Groth16TypeI.Stmt
prover : Prover F Groth16TypeI
t : Polynomial F := ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))
h0012 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2) 0
h0021 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1) 0
h0022 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2) 0
h0112 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2) 0
h0121 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1) 0
h0122 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2) 0
h0212 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2) 0
h0221 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1) 0
h0222 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2) 0
h1022 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2) 0
h1112 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2) 0
h1121 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1) 0
h1122 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2)
      (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum) +
                      (-(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              (List.map
                                  (fun x =>
                                    Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                  (List.finRange n_var)).sum) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    (List.map
                                        (fun x =>
                                          Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                            Polynomial.X ^ ↑x)
                                        (List.finRange n_var)).sum) +
                            -(monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum))))))) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                        (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                      (-(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            ((List.map
                                  (fun x =>
                                    Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                      (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                  (List.finRange (n_var - 1))).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                        (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                        (List.finRange n_stmt)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                          (-(monomial
                                    ((fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                              -(monomial
                                    ((fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                                  ((List.map
                                        (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                        (List.finRange n_wit)).sum *
                                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
                            -(monomial
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ))))))))) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))))
                      (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                    (-(monomial
                            ((fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                          ((List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                      (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                        (-(monomial
                                  ((fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                            -(monomial
                                  ((fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                                ((List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
                          -(monomial
                                ((fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ))))))))) +
          (-(monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
            (-(monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
              (-(monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                (-(monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                      ((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                  (-(monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                        ((List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                    (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map
                                    (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                      (-(monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                          -(monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))))
                              ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
                        -(monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))
                            ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β))))))))) +
        ((monomial
              ((fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))))))
            1 +
          ((monomial
                    ((fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum +
                (monomial
                    ((fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))))
                  (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum +
              (monomial ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))))
                (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum +
            ((monomial
                  ((fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
              ((monomial
                    ((fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                  (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
                ((monomial
                      ((fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))))
                    (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
                  ((monomial
                        ((fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                      (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum +
                    ((monomial
                          ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum +
                      ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum +
                          (monomial
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum +
                        ((monomial
                                ((fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum +
                            (monomial
                                ((fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))))
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum +
                          (monomial
                              ((fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))))
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum)))))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2) 0
hA1011 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0111 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0012 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0011 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0010 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0101 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA1001 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0001 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0110 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA1010 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hA0021 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB1011 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0111 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0012 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0011 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0010 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0101 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB1001 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0001 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0110 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB1010 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hB0021 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC1011 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0111 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0012 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0011 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0010 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0101 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC1001 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0001 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0110 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC1010 :
  coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
hC0021 :
  coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1)))
          (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
            (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)) +
            ((monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum +
              ((monomial fun₀ | Vars.γ => 1)
                  (List.map
                      (fun x =>
                        Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                          (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                      (List.finRange (n_var - 1))).sum +
                ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                            (List.finRange n_stmt)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                            (List.finRange n_stmt)).sum +
                    (monomial fun₀ | Vars.δ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                          (List.finRange n_stmt)).sum +
                  ((monomial ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                            (List.finRange n_wit)).sum +
                      (monomial ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1))
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                            (List.finRange n_wit)).sum +
                    (monomial fun₀ | Vars.γ => 1)
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                          (List.finRange n_wit)).sum))))))) =
    coeff ((((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1)
      ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))
          (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)) +
        ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))
            (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)) +
          ((monomial ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))
              (Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)) +
            (monomial ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))
              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum)))
⊢ ((List.map (fun i => Polynomial.C (stmt i) * u_stmt i) (List.finRange n_stmt)).sum +
        (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q i)) * u_wit i)
            (List.finRange n_wit)).sum) *
      ((List.map (fun i => Polynomial.C (stmt i) * v_stmt i) (List.finRange n_stmt)).sum +
        (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q i)) * v_wit i)
            (List.finRange n_wit)).sum) =
    (List.map (fun i => Polynomial.C (stmt i) * w_stmt i) (List.finRange n_stmt)).sum +
        (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q i)) * w_wit i)
            (List.finRange n_wit)).sum +
      (List.map
          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) * (Polynomial.X ^ ↑x * t))
          (List.finRange (n_var - 1))).sum
Tactic:
simp only [coeff_monomial, coeff_add, coeff_neg, coeff_zero] at h0012 h0021 h0022 h0112 h0121 h0122 h0212 h0221 h0222 h1022 h1112 h1121 h1122 hA1011 hA0111 hA0012 hA0011 hA0010 hA0101 hA1001 hA0001 hA0110 hA1010 hA0021 hB1011 hB0111 hB0012 hB0011 hB0010 hB0101 hB1001 hB0001 hB0110 hB1010 hB0021 hC1011 hC0111 hC0012 hC0011 hC0010 hC0101 hC1001 hC0001 hC0110 hC1010 hC0021
Proof state after:
case intro.intro.intro
F : Type
inst✝ : Field F
n_stmt n_wit n_var : ℕ
u_stmt : Fin n_stmt → Polynomial F
u_wit : Fin n_wit → Polynomial F
v_stmt : Fin n_stmt → Polynomial F
v_wit : Fin n_wit → Polynomial F
w_stmt : Fin n_stmt → Polynomial F
w_wit : Fin n_wit → Polynomial F
r : Fin n_wit → F
stmt : Groth16TypeI.Stmt
prover : Prover F Groth16TypeI
t : Polynomial F := ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))
h0012 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0021 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0022 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0112 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0121 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0122 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0212 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0221 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h0222 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 2) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h1022 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h1112 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h1121 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 1 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 1 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 1 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 1 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
h1122 :
  (-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            (List.map
                                (fun x =>
                                  Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                                (List.finRange n_var)).sum
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1)) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  (List.map
                                      (fun x =>
                                        Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                          Polynomial.X ^ ↑x)
                                      (List.finRange n_var)).sum
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                (List.map
                                    (fun x =>
                                      Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) *
                                        Polynomial.X ^ ↑x)
                                    (List.finRange n_var)).sum
                            else 0)))))) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.α => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.β => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) +
                              ((fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                      else 0) +
                    ((-if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map
                                (fun x =>
                                  Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                    (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                                (List.finRange (n_var - 1))).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                        else 0) +
                      ((((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.δ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                      (List.finRange n_stmt)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0) +
                        (((-if
                                  (fun₀ | Vars.β => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                            -if
                                  (fun₀ | Vars.α => 1) +
                                      ((fun₀ | Vars.γ => 1) +
                                        ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                      fun₀ | Vars.δ => 2 then
                                (List.map
                                      (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                      (List.finRange n_wit)).sum *
                                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                              else 0) +
                          -if
                                (fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
                            else 0))))))) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.β => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) +
                            ((fun₀ | Vars.δ => 1) +
                              ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                  (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                              (List.finRange (n_var - 1))).sum *
                          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                      else 0) +
                    ((((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.δ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                    (List.finRange n_stmt)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.δ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0) +
                      (((-if
                                (fun₀ | Vars.β => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                          -if
                                (fun₀ | Vars.α => 1) +
                                    ((fun₀ | Vars.γ => 1) +
                                      ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                    fun₀ | Vars.δ => 2 then
                              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                    (List.finRange n_wit)).sum *
                                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                            else 0) +
                        -if
                              (fun₀ | Vars.γ => 1) +
                                  ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
                          else 0))))))) +
        ((-if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α) *
                Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
            else 0) +
          ((-if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β) *
                  Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
              else 0) +
            ((-if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ) *
                    Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                else 0) +
              ((-if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                  else 0) +
                ((-if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                                (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                            (List.finRange (n_var - 1))).sum *
                        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                    else 0) +
                  ((((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                                  (List.finRange n_stmt)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                                (List.finRange n_stmt)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0) +
                    (((-if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                        -if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                          else 0) +
                      -if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
                        else 0))))))) +
      ((if
            (fun₀ | Vars.γ => 1) +
                ((fun₀ | Vars.δ => 1) +
                  ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1)))) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
          1
        else 0) +
        ((((if
                  (fun₀ | Vars.β => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * u_stmt x) (List.finRange n_stmt)).sum
              else 0) +
              if
                  (fun₀ | Vars.α => 1) +
                      ((fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                (List.map (fun x => Polynomial.C (stmt x) * v_stmt x) (List.finRange n_stmt)).sum
              else 0) +
            if
                (fun₀ | Vars.δ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1)) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (stmt x) * w_stmt x) (List.finRange n_stmt)).sum
            else 0) +
          ((if
                (fun₀ | Vars.γ => 1) +
                    ((fun₀ | Vars.δ => 1) +
                      ((fun₀ | Vars.α => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
              Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) +
                      ((fun₀ | Vars.δ => 1) +
                        ((fun₀ | Vars.β => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
              else 0) +
              ((if
                    (fun₀ | Vars.γ => 1) +
                        ((fun₀ | Vars.δ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)))) =
                      (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                  Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
                else 0) +
                ((if
                      (fun₀ | Vars.γ => 1) +
                          ((fun₀ | Vars.δ => 1) +
                            ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                    (List.map
                        (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum
                  else 0) +
                  ((if
                        (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 2 then
                      (List.map
                          (fun x =>
                            Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                              (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                          (List.finRange (n_var - 1))).sum
                    else 0) +
                    ((((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.δ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                                (List.finRange n_stmt)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.δ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                              (List.finRange n_stmt)).sum
                        else 0) +
                      (((if
                              (fun₀ | Vars.β => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                          if
                              (fun₀ | Vars.α => 1) +
                                  ((fun₀ | Vars.γ => 1) +
                                    ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1))) =
                                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                  fun₀ | Vars.δ => 2 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                                (List.finRange n_wit)).sum
                          else 0) +
                        if
                            (fun₀ | Vars.γ => 1) +
                                ((fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1)) =
                              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 2) +
                                fun₀ | Vars.δ => 2 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                              (List.finRange n_wit)).sum
                        else 0))))))))) =
    0
hA1011 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0111 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0012 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0011 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0010 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0101 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA1001 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0001 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0110 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA1010 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hA0021 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.A (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.A SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.A (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB1011 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0111 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0012 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0011 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0010 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0101 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB1001 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0001 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0110 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB1010 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hB0021 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC1011 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0111 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0012 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 2 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0011 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0010 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0101 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC1001 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0001 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 0) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0110 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC1010 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 1) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
hC0021 :
  (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.α => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.α)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.β)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.1 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          ((if
                ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                  (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum
            else 0) +
            ((if
                  (fun₀ | Vars.γ => 1) =
                    (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                (List.map
                    (fun x =>
                      Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) *
                        (Polynomial.X ^ ↑x * ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))))
                    (List.finRange (n_var - 1))).sum
              else 0) +
              ((((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * u_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.δ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * v_stmt x)
                          (List.finRange n_stmt)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.δ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.y x)) * w_stmt x)
                        (List.finRange n_stmt)).sum
                  else 0) +
                (((if
                        ((fun₀ | Vars.β => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * u_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                    if
                        ((fun₀ | Vars.α => 1) + fun₀ | Vars.γ => 1) =
                          (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                      (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * v_wit x)
                          (List.finRange n_wit)).sum
                    else 0) +
                  if
                      (fun₀ | Vars.γ => 1) =
                        (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q x)) * w_wit x)
                        (List.finRange n_wit)).sum
                  else 0)))))) =
    (if
          (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.β => 1) =
            (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
        Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.β)
      else 0) +
      ((if
            (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.γ => 1) =
              (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
          Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (fun₀ | Vars.γ => 1) + ((fun₀ | Vars.δ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            Polynomial.C (prover.2 Proof_Idx.C SRS_Elements_Idx.δ)
          else 0) +
          if
              ((fun₀ | Vars.γ => 1) + fun₀ | Vars.δ => 1) =
                (((fun₀ | Vars.α => 0) + fun₀ | Vars.β => 0) + fun₀ | Vars.γ => 2) + fun₀ | Vars.δ => 1 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.C (SRS_Elements_Idx.x_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0))
⊢ ((List.map (fun i => Polynomial.C (stmt i) * u_stmt i) (List.finRange n_stmt)).sum +
        (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q i)) * u_wit i)
            (List.finRange n_wit)).sum) *
      ((List.map (fun i => Polynomial.C (stmt i) * v_stmt i) (List.finRange n_stmt)).sum +
        (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q i)) * v_wit i)
            (List.finRange n_wit)).sum) =
    (List.map (fun i => Polynomial.C (stmt i) * w_stmt i) (List.finRange n_stmt)).sum +
        (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.q i)) * w_wit i)
            (List.finRange n_wit)).sum +
      (List.map
          (fun x => Polynomial.C (prover.1 Proof_Idx.C (SRS_Elements_Idx.x_pow_times_t x)) * (Polynomial.X ^ ↑x * t))
          (List.finRange (n_var - 1))).sum