Theorem: BabySNARK.is_sound (FormalSnarksProject/SNARKs/BabySnark.lean)

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
t : Polynomial F
ht : (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum = t
ht0 : t.Monic
stmt : BabySNARK.Stmt
prover : Prover F BabySNARK
hI_00 :
  ((if
              (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
                0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                  (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 0 else 0) + if False then 0 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 0 else 0) + if True then 0 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                    (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
              0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
              0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                            (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 0 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 0 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 0 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 0 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 0 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 0 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 0 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 0 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 0 else 0) + if False then 0 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 0 else 0) + if True then 0 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 0 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 0 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 0 else 0) + if False then 0 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 0 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 0 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 0 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 0 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 0 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 0 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                        (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
                      0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 0 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 0 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                            (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
                    0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
                    0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                      (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 0 else 0) + if False then 0 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 0 else 0) + if True then 0 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                        (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
                  0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_01 :
  ((if
              (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
                0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                  (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 0 else 0) + if False then 1 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 0 else 0) + if True then 1 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                    (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
              0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
              0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                            (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 1 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 1 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 1 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 1 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 1 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 1 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 1 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 1 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 0 else 0) + if False then 1 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 0 else 0) + if True then 1 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 1 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 1 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 0 else 0) + if False then 1 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 0 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 1 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 1 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 1 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 1 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 1 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                        (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
                      0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 1 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 1 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                            (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
                    0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
                    0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                      (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 0 else 0) + if False then 1 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 0 else 0) + if True then 1 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                        (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
                  0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_02 :
  ((if
              (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
                0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                  (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 0 else 0) + if False then 2 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 0 else 0) + if True then 2 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                    (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
              0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
              0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                            (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 2 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 2 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 2 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 2 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 2 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 2 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 2 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 2 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 0 else 0) + if False then 2 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 0 else 0) + if True then 2 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 0 else 0) + if False then 2 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 0 else 0) + if True then 2 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 0 else 0) + if False then 2 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 0 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 2 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 2 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 2 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 0 else 0) + if False then 2 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 0 else 0) + if True then 2 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                        (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
                      0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 0 else 0) + if False then 2 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 0 else 0) + if True then 2 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                            (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
                    0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
                    0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                      (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 0 else 0) + if False then 2 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 0 else 0) + if True then 2 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                        (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
                  0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_10 :
  ((if
              (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
                0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                  (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 1 else 0) + if False then 0 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 1 else 0) + if True then 0 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                    (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
              0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
              0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                            (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 0 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 0 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 0 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 0 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 0 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 0 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 0 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 0 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 1 else 0) + if False then 0 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 1 else 0) + if True then 0 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 0 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 0 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 1 else 0) + if False then 0 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 1 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 0 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 0 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 0 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 0 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 0 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                        (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
                      0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 0 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 0 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                            (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
                    0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
                    0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                      (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 1 else 0) + if False then 0 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 1 else 0) + if True then 0 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                        (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
                  0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_11 :
  ((if
              (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
                0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                  (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 1 else 0) + if False then 1 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 1 else 0) + if True then 1 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                    (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
              0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
              0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                            (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 1 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 1 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 1 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 1 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 1 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 1 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 1 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 1 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 1 else 0) + if False then 1 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 1 else 0) + if True then 1 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 1 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 1 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 1 else 0) + if False then 1 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 1 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 1 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 1 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 1 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 1 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 1 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                        (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
                      0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 1 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 1 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                            (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
                    0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
                    0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                      (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 1 else 0) + if False then 1 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 1 else 0) + if True then 1 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                        (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
                  0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_12 :
  ((if
              (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
                0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                  (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 1 else 0) + if False then 2 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 1 else 0) + if True then 2 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                    (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
              0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
              0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                            (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 2 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 2 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 2 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 2 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 2 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 2 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 2 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 2 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 1 else 0) + if False then 2 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 1 else 0) + if True then 2 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 1 else 0) + if False then 2 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 1 else 0) + if True then 2 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 1 else 0) + if False then 2 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 1 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 2 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 2 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 2 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 1 else 0) + if False then 2 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 1 else 0) + if True then 2 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                        (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
                      0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 1 else 0) + if False then 2 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 1 else 0) + if True then 2 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                            (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
                    0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
                    0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                      (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 1 else 0) + if False then 2 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 1 else 0) + if True then 2 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                        (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
                  0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_20 :
  ((if
              (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
                0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                  (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 2 else 0) + if False then 0 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 2 else 0) + if True then 0 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                    (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
              0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
              0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                            (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 0 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 0 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 0 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 0 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 0 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 0 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 0 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 0 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 2 else 0) + if False then 0 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 2 else 0) + if True then 0 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 0 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 0 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 2 else 0) + if False then 0 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 2 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 0 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 0 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 0 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 0 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 0 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 0 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                        (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
                      0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 0 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 0 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                            (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
                    0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
                    0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                      (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 2 else 0) + if False then 0 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 2 else 0) + if True then 0 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                        (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
                  0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_21 :
  ((if
              (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
                0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                  (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 2 else 0) + if False then 1 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 2 else 0) + if True then 1 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                    (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
              0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
              0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                            (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 1 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 1 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 1 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 1 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 1 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 1 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 1 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 1 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 2 else 0) + if False then 1 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 2 else 0) + if True then 1 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 1 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 1 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 2 else 0) + if False then 1 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 2 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 1 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 1 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 1 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 1 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 1 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 1 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                        (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
                      0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 1 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 1 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                            (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
                    0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
                    0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                      (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 2 else 0) + if False then 1 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 2 else 0) + if True then 1 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                        (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
                  0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hI_22 :
  ((if
              (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
                0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
          else 0) +
          ((if
                ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                  (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
            else 0) +
            ((if
                  (((if False then 1 else 0) + if True then 1 else 0) =
                      (if True then 2 else 0) + if False then 2 else 0) ∧
                    ((if True then 1 else 0) + if False then 1 else 0) =
                      (if False then 2 else 0) + if True then 2 else 0 then
                Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0) +
              if
                  ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                    (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                      (List.finRange n_wit)).sum *
                  (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
              else 0)) +
        if
            (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
              0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
      ((if
            (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
              0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum
        else 0) +
        (((-if
                          ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                            (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum
                      else 0) +
                    ((-if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 2 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 2 else 0) ∧
                                (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 2 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0) +
                        -if
                              (((if True then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 2 else 0) ∧
                                ((if False then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 2 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum
                          else 0)) +
                  -if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum
                    else 0) +
                ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 2 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 2 else 0 then
                        (List.map
                              (fun x =>
                                Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                      else 0) +
                    ((-if
                            ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 2 else 0) ∧
                              (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                        else 0) +
                      ((-if
                              ((if False then 1 else 0) +
                                    ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                                  (if True then 2 else 0) + if False then 2 else 0) ∧
                                (if True then 1 else 0) +
                                    ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                                  (if False then 2 else 0) + if True then 2 else 0 then
                            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0) +
                        -if
                              ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0) =
                                  (if True then 2 else 0) + if False then 2 else 0) ∧
                                (if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0) =
                                  (if False then 2 else 0) + if True then 2 else 0 then
                            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                  (List.finRange n_wit)).sum *
                              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                          else 0)) +
                  -if
                        (((if False then 1 else 0) + if True then 1 else 0) =
                            (if True then 2 else 0) + if False then 2 else 0) ∧
                          ((if True then 1 else 0) + if False then 1 else 0) =
                            (if False then 2 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
                    else 0) +
              ((-if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                      (List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                    else 0) +
                  ((-if
                          (((if True then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 2 else 0) ∧
                            ((if False then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 2 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                      else 0) +
                    ((-if
                            ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 2 else 0) ∧
                              (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 2 else 0 then
                          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0) +
                      -if
                            (((if True then 1 else 0) + if True then 1 else 0) =
                                (if True then 2 else 0) + if False then 2 else 0) ∧
                              ((if False then 1 else 0) + if False then 1 else 0) =
                                (if False then 2 else 0) + if True then 2 else 0 then
                          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                        else 0)) +
                -if
                      ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                        (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                    (List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
                  else 0) +
            ((if
                    (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
                      0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
                  -((List.map
                          (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum)
                else 0) +
                ((-if
                        ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                          (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                      Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum
                    else 0) +
                  ((-if
                          (((if False then 1 else 0) + if True then 1 else 0) =
                              (if True then 2 else 0) + if False then 2 else 0) ∧
                            ((if True then 1 else 0) + if False then 1 else 0) =
                              (if False then 2 else 0) + if True then 2 else 0 then
                        Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0) +
                    -if
                          ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                            (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          (List.map
                              (fun x =>
                                Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                              (List.finRange n_var)).sum
                      else 0)) +
              if
                  (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
                    0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum)
              else 0) +
          ((if
                  (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
                    0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum
              else 0) +
              ((if
                    ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                      (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                  Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum
                else 0) +
                ((if
                      (((if False then 1 else 0) + if True then 1 else 0) =
                          (if True then 2 else 0) + if False then 2 else 0) ∧
                        ((if True then 1 else 0) + if False then 1 else 0) =
                          (if False then 2 else 0) + if True then 2 else 0 then
                    Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0) +
                  if
                      ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                        (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
                    (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum *
                      (List.map
                          (fun x =>
                            -(Polynomial.C
                                  (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                                Polynomial.X ^ ↑x))
                          (List.finRange n_var)).sum
                  else 0)) +
            if
                (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
                  0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
              (List.map
                    (fun x =>
                      Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum
            else 0))) =
    0
hII_00 :
  (if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 0 else 0) + if False then 0 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 0 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 0 else 0) + if False then 0 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 0 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 0 else 0) + if False then 0 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 0 else 0) + if True then 0 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 0 else 0) + if False then 0 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_01 :
  (if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 0 else 0) + if False then 1 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 1 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 0 else 0) + if False then 1 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 0 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 0 else 0) + if False then 1 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 0 else 0) + if True then 1 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 0 else 0) + if False then 1 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_02 :
  (if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 0 else 0) + if False then 2 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 2 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 0 else 0) + if False then 2 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 0 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 0 else 0) + if False then 2 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 0 else 0) + if True then 2 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 0 else 0) + if False then 2 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 0 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_10 :
  (if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 1 else 0) + if False then 0 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 0 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 1 else 0) + if False then 0 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 1 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 1 else 0) + if False then 0 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 1 else 0) + if True then 0 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 1 else 0) + if False then 0 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_11 :
  (if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 1 else 0) + if False then 1 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 1 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 1 else 0) + if False then 1 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 1 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 1 else 0) + if False then 1 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 1 else 0) + if True then 1 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 1 else 0) + if False then 1 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_12 :
  (if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 1 else 0) + if False then 2 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 2 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 1 else 0) + if False then 2 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 1 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 1 else 0) + if False then 2 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 1 else 0) + if True then 2 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 1 else 0) + if False then 2 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 1 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_20 :
  (if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 2 else 0) + if False then 0 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 0 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 2 else 0) + if False then 0 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 2 else 0) + if True then 0 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 2 else 0) + if False then 0 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 2 else 0) + if True then 0 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 2 else 0) + if False then 0 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 0 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_21 :
  (if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 2 else 0) + if False then 1 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 1 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 2 else 0) + if False then 1 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 2 else 0) + if True then 1 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 2 else 0) + if False then 1 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 2 else 0) + if True then 1 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 2 else 0) + if False then 1 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 1 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hII_22 :
  (if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum
        else 0) +
        ((if
              (((if True then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if False then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
          else 0) +
          ((if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 2 else 0) + if False then 2 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
            else 0) +
            if
                (((if True then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                  ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 2 else 0 then
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum
            else 0)) +
      ((((-if
                  ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                      (if True then 2 else 0) + if False then 2 else 0) ∧
                    (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                      (if False then 2 else 0) + if True then 2 else 0 then
                (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum
              else 0) +
            -if
                  ((if False then 1 else 0) +
                        ((if True then 1 else 0) + ((if False then 1 else 0) + if True then 1 else 0)) =
                      (if True then 2 else 0) + if False then 2 else 0) ∧
                    (if True then 1 else 0) +
                        ((if False then 1 else 0) + ((if True then 1 else 0) + if False then 1 else 0)) =
                      (if False then 2 else 0) + if True then 2 else 0 then
                Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
              else 0) +
          -if
                ((if False then 1 else 0) + ((if True then 1 else 0) + if True then 1 else 0) =
                    (if True then 2 else 0) + if False then 2 else 0) ∧
                  (if True then 1 else 0) + ((if False then 1 else 0) + if False then 1 else 0) =
                    (if False then 2 else 0) + if True then 2 else 0 then
              Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
            else 0) +
        -if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum
          else 0) =
    0
hH_00 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_01 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_02 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_10 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_11 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_12 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_20 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_21 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hH_22 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_00 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_01 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_02 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_10 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_11 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_12 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_20 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_21 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hV_22 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_00 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_01 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_02 :
  (if
          (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 0 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 0 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 0 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 0 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 0 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_10 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_11 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_12 :
  (if
          (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 1 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 1 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 1 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 1 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 1 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_20 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 0 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 0 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 0 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 0 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 0 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_21 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 1 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 1 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 1 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 1 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 1 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0))
hB_22 :
  (if
          (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum
          else 0)) =
    (if
          (0 Vars.β = (if True then 2 else 0) + if False then 2 else 0) ∧
            0 Vars.γ = (if False then 2 else 0) + if True then 2 else 0 then
        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum
      else 0) +
      ((if
            ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
              (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
          Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ)
        else 0) +
        ((if
              (((if False then 1 else 0) + if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                ((if True then 1 else 0) + if False then 1 else 0) =
                  (if False then 2 else 0) + if True then 2 else 0 then
            Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ)
          else 0) +
          if
              ((if True then 1 else 0) = (if True then 2 else 0) + if False then 2 else 0) ∧
                (if False then 1 else 0) = (if False then 2 else 0) + if True then 2 else 0 then
            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).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.B (SRS_Elements_Idx.βu i)) * u_wit i)
              (List.finRange n_wit)).sum) ^
        2 -
      1 =
    t *
      (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu i)) * u_wit i)
          (List.finRange n_wit)).sum
Tactic:
simp (config := {decide := true}) only [ite_false, ite_true] at hI_00 hI_01 hI_02 hI_10 hI_11 hI_12 hI_20 hI_21 hI_22 hII_00 hII_01 hII_02 hII_10 hII_11 hII_12 hII_20 hII_21 hII_22 hH_00 hH_01 hH_02 hH_10 hH_11 hH_12 hH_20 hH_21 hH_22 hV_00 hV_01 hV_02 hV_10 hV_11 hV_12 hV_20 hV_21 hV_22 hB_00 hB_01 hB_02 hB_10 hB_11 hB_12 hB_20 hB_21 hB_22
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
t : Polynomial F
ht : (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum = t
ht0 : t.Monic
stmt : BabySNARK.Stmt
prover : Prover F BabySNARK
hI_00 :
  (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                (List.finRange n_var)).sum *
            (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum +
          (0 + (0 + 0)) +
        (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
          (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum +
      ((List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum *
          (List.map (fun x => Polynomial.C (if ↑x = 0 then 1 else 0) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum +
        (-0 + (-0 + (-0 + -0)) + -0 + (-0 + (-0 + (-0 + -0)) + -0) + (-0 + (-0 + (-0 + -0)) + -0) +
            (-((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    (List.map
                        (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum) +
                (-0 + (-0 + -0)) +
              -((List.map
                      (fun x =>
                        Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum *
                  (List.map
                      (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                      (List.finRange n_var)).sum)) +
          ((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                    (List.finRange n_var)).sum *
                (List.map
                    (fun x =>
                      -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                          Polynomial.X ^ ↑x))
                    (List.finRange n_var)).sum +
              (0 + (0 + 0)) +
            (List.map
                  (fun x =>
                    Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                      Polynomial.X ^ ↑x)
                  (List.finRange n_var)).sum *
              (List.map
                  (fun x =>
                    -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                        Polynomial.X ^ ↑x))
                  (List.finRange n_var)).sum))) =
    0
hI_01 hI_02 :
  0 + (0 + (0 + 0)) + 0 +
      (0 +
        (-0 + (-0 + (-0 + -0)) + -0 + (-0 + (-0 + (-0 + -0)) + -0) + (-0 + (-0 + (-0 + -0)) + -0) +
            (0 + (-0 + (-0 + -0)) + 0) +
          (0 + (0 + (0 + 0)) + 0))) =
    0
hI_10 :
  0 +
          (Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) *
              (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum +
            (0 +
              (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
                    (List.finRange n_wit)).sum *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum)) +
        0 +
      (0 +
        (-((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum) +
                    (-0 + (-0 + -0)) +
                  -((List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                          (List.finRange n_wit)).sum) +
                (-0 + (-0 + (-0 + -0)) + -0) +
              (-((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)) +
                  (-0 + (-0 + -0)) +
                -((List.map
                        (fun x =>
                          Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x)
                        (List.finRange n_var)).sum *
                    Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ))) +
            (0 +
                (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                      (List.map
                          (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum) +
                  (-0 +
                    -((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                            (List.finRange n_wit)).sum *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum))) +
              0) +
          (0 +
              (Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                  (List.map
                      (fun x =>
                        -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                            Polynomial.X ^ ↑x))
                      (List.finRange n_var)).sum +
                (0 +
                  (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                        (List.finRange n_wit)).sum *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum)) +
            0))) =
    0
hI_11 :
  0 +
          (0 +
            (Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) *
                (List.map (fun x => Polynomial.C (t.coeff ↑x) * Polynomial.X ^ ↑x) (List.finRange n_var)).sum +
              0)) +
        0 +
      (0 +
        (-0 + (-0 + (-0 + -0)) + -0 +
                (-((List.map
                            (fun x =>
                              Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)) +
                    (-0 + (-0 + -0)) +
                  -((List.map
                          (fun x =>
                            Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x)
                          (List.finRange n_var)).sum *
                      Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ))) +
              (-0 + (-0 + (-0 + -0)) + -0) +
            (0 +
                (-0 +
                  (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                        (List.map
                            (fun x =>
                              Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
                            (List.finRange n_var)).sum) +
                    -0)) +
              0) +
          (0 +
              (0 +
                (Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                    (List.map
                        (fun x =>
                          -(Polynomial.C (List.map (fun j => stmt j * (u_stmt j).coeff ↑x) (List.finRange n_stmt)).sum *
                              Polynomial.X ^ ↑x))
                        (List.finRange n_var)).sum +
                  0)) +
            0))) =
    0
hI_12 :
  0 + (0 + (0 + 0)) + 0 +
      (0 +
        (-0 + (-0 + (-0 + -0)) + -0 + (-0 + (-0 + (-0 + -0)) + -0) + (-0 + (-0 + (-0 + -0)) + -0) +
            (0 + (-0 + (-0 + -0)) + 0) +
          (0 + (0 + (0 + 0)) + 0))) =
    0
hI_20 :
  0 + (0 + (0 + 0)) + 0 +
      (0 +
        (-0 +
                    (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum) +
                      (-0 +
                        -((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum))) +
                  -0 +
                (-0 + (-0 + (-0 + -0)) + -0) +
              (-0 +
                  (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                        Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)) +
                    (-0 +
                      -((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                              (List.finRange n_wit)).sum *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)))) +
                -0) +
            (0 + (-0 + (-0 + -0)) + 0) +
          (0 + (0 + (0 + 0)) + 0))) =
    0
hI_21 :
  0 + (0 + (0 + 0)) + 0 +
      (0 +
        (-0 +
                    (-0 +
                      (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum) +
                        -0)) +
                  -0 +
                (-0 +
                    (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)) +
                      (-0 +
                        -((List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                                (List.finRange n_wit)).sum *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)))) +
                  -0) +
              (-0 +
                  (-0 +
                    (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                          Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ)) +
                      -0)) +
                -0) +
            (0 + (-0 + (-0 + -0)) + 0) +
          (0 + (0 + (0 + 0)) + 0))) =
    0
hI_22 :
  0 + (0 + (0 + 0)) + 0 +
      (0 +
        (-0 + (-0 + (-0 + -0)) + -0 +
                (-0 +
                    (-0 +
                      (-(Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) *
                            Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ)) +
                        -0)) +
                  -0) +
              (-0 + (-0 + (-0 + -0)) + -0) +
            (0 + (-0 + (-0 + -0)) + 0) +
          (0 + (0 + (0 + 0)) + 0))) =
    0
hII_00 hII_01 hII_02 : 0 + (0 + (0 + 0)) + (-0 + -0 + -0 + -0) = 0
hII_10 :
  (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
            (List.finRange n_var)).sum +
        (0 + (0 + 0)) +
      (-0 + -0 + -0 + -0) =
    0
hII_11 :
  0 + (0 + (0 + 0)) +
      (-0 + -0 + -0 +
        -(List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
              (List.finRange n_var)).sum) =
    0
hII_12 : 0 + (0 + (0 + 0)) + (-0 + -0 + -0 + -0) = 0
hII_20 :
  0 +
        (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ) +
          (0 +
            (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
                (List.finRange n_wit)).sum)) +
      (-0 + -0 + -0 + -0) =
    0
hII_21 :
  0 + (0 + (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ) + 0)) +
      (-(List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
                  (List.finRange n_wit)).sum +
            -0 +
          -Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ) +
        -0) =
    0
hII_22 : 0 + (0 + (0 + 0)) + (-0 + -Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ) + -0 + -0) = 0
hH_00 :
  (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
          (List.finRange n_var)).sum +
      (0 + (0 + 0)) =
    (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
          (List.finRange n_var)).sum +
      (0 + (0 + 0))
hH_01 hH_02 : True
hH_10 :
  0 +
      (Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γ) +
        (0 +
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
              (List.finRange n_wit)).sum)) =
    0 +
      (Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γ) +
        (0 +
          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.H (SRS_Elements_Idx.βu x)) * u_wit x)
              (List.finRange n_wit)).sum))
hH_11 :
  0 + (0 + (Polynomial.C (prover.1 Proof_Idx.H SRS_Elements_Idx.γβ) + 0)) =
    0 + (0 + (Polynomial.C (prover.2 Proof_Idx.H SRS_Elements_Idx.γβ) + 0))
hH_12 hH_20 hH_21 hH_22 : True
hV_00 :
  (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
          (List.finRange n_var)).sum +
      (0 + (0 + 0)) =
    (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
          (List.finRange n_var)).sum +
      (0 + (0 + 0))
hV_01 hV_02 : True
hV_10 :
  0 +
      (Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γ) +
        (0 +
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
              (List.finRange n_wit)).sum)) =
    0 +
      (Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γ) +
        (0 +
          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.V (SRS_Elements_Idx.βu x)) * u_wit x)
              (List.finRange n_wit)).sum))
hV_11 :
  0 + (0 + (Polynomial.C (prover.1 Proof_Idx.V SRS_Elements_Idx.γβ) + 0)) =
    0 + (0 + (Polynomial.C (prover.2 Proof_Idx.V SRS_Elements_Idx.γβ) + 0))
hV_12 hV_20 hV_21 hV_22 : True
hB_00 :
  (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
          (List.finRange n_var)).sum +
      (0 + (0 + 0)) =
    (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.τ_pow x)) * Polynomial.X ^ ↑x)
          (List.finRange n_var)).sum +
      (0 + (0 + 0))
hB_01 hB_02 : True
hB_10 :
  0 +
      (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γ) +
        (0 +
          (List.map (fun x => Polynomial.C (prover.1 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
              (List.finRange n_wit)).sum)) =
    0 +
      (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γ) +
        (0 +
          (List.map (fun x => Polynomial.C (prover.2 Proof_Idx.B (SRS_Elements_Idx.βu x)) * u_wit x)
              (List.finRange n_wit)).sum))
hB_11 :
  0 + (0 + (Polynomial.C (prover.1 Proof_Idx.B SRS_Elements_Idx.γβ) + 0)) =
    0 + (0 + (Polynomial.C (prover.2 Proof_Idx.B SRS_Elements_Idx.γβ) + 0))
hB_12 hB_20 hB_21 hB_22 : True
⊢ ((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.B (SRS_Elements_Idx.βu i)) * u_wit i)
              (List.finRange n_wit)).sum) ^
        2 -
      1 =
    t *
      (List.map (fun i => Polynomial.C (prover.1 Proof_Idx.H (SRS_Elements_Idx.βu i)) * u_wit i)
          (List.finRange n_wit)).sum