Theorem: Lipmaa.soundness
Proof state before:
case mt.hs
F : Type
inst✝ : Field F
n_stmt n_wit n_var : ℕ
u_stmt : Fin n_stmt → Polynomial F
u_wit : Fin n_wit → Polynomial F
v_stmt : Fin n_stmt → Polynomial F
v_wit : Fin n_wit → Polynomial F
w_stmt : Fin n_stmt → Polynomial F
w_wit : Fin n_wit → Polynomial F
r : Fin n_wit → F
stmt : Lipmaa.Stmt
prover : Prover F Lipmaa
t : Polynomial F := ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))
eqn :
  (List.map
        (fun pairing =>
          ((List.map
                  (fun pf_elem =>
                    C (Lipmaa.verificationPairingProof_G1 stmt () pairing pf_elem) *
                      (List.map (fun SRS_elem => C (prover.1 pf_elem SRS_elem) * Lipmaa.SRSElementValue_G1 SRS_elem)
                          Lipmaa.ListSRSElements_G1).sum)
                  Lipmaa.ListProof_G1).sum +
              (List.map
                  (fun SRS_elem =>
                    C (Lipmaa.verificationPairingSRS_G1 stmt () pairing SRS_elem) * Lipmaa.SRSElementValue_G1 SRS_elem)
                  Lipmaa.ListSRSElements_G1).sum) *
            ((List.map
                  (fun pf_elem =>
                    C (Lipmaa.verificationPairingProof_G2 stmt () pairing pf_elem) *
                      (List.map (fun SRS_elem => C (prover.2 pf_elem SRS_elem) * Lipmaa.SRSElementValue_G2 SRS_elem)
                          Lipmaa.ListSRSElements_G2).sum)
                  Lipmaa.ListProof_G2).sum +
              (List.map
                  (fun SRS_elem =>
                    C (Lipmaa.verificationPairingSRS_G2 stmt () pairing SRS_elem) * Lipmaa.SRSElementValue_G2 SRS_elem)
                  Lipmaa.ListSRSElements_G2).sum))
        (Lipmaa.ListPairings ())).sum =
    0
⊢ ∀ i ∈ Finset.univ, (Polynomial.X - Polynomial.C (r i)).Monic
Tactic:
intro i hi
Proof state after:
case mt.hs
F : Type
inst✝ : Field F
n_stmt n_wit n_var : ℕ
u_stmt : Fin n_stmt → Polynomial F
u_wit : Fin n_wit → Polynomial F
v_stmt : Fin n_stmt → Polynomial F
v_wit : Fin n_wit → Polynomial F
w_stmt : Fin n_stmt → Polynomial F
w_wit : Fin n_wit → Polynomial F
r : Fin n_wit → F
stmt : Lipmaa.Stmt
prover : Prover F Lipmaa
t : Polynomial F := ∏ i : Fin n_wit, (Polynomial.X - Polynomial.C (r i))
eqn :
  (List.map
        (fun pairing =>
          ((List.map
                  (fun pf_elem =>
                    C (Lipmaa.verificationPairingProof_G1 stmt () pairing pf_elem) *
                      (List.map (fun SRS_elem => C (prover.1 pf_elem SRS_elem) * Lipmaa.SRSElementValue_G1 SRS_elem)
                          Lipmaa.ListSRSElements_G1).sum)
                  Lipmaa.ListProof_G1).sum +
              (List.map
                  (fun SRS_elem =>
                    C (Lipmaa.verificationPairingSRS_G1 stmt () pairing SRS_elem) * Lipmaa.SRSElementValue_G1 SRS_elem)
                  Lipmaa.ListSRSElements_G1).sum) *
            ((List.map
                  (fun pf_elem =>
                    C (Lipmaa.verificationPairingProof_G2 stmt () pairing pf_elem) *
                      (List.map (fun SRS_elem => C (prover.2 pf_elem SRS_elem) * Lipmaa.SRSElementValue_G2 SRS_elem)
                          Lipmaa.ListSRSElements_G2).sum)
                  Lipmaa.ListProof_G2).sum +
              (List.map
                  (fun SRS_elem =>
                    C (Lipmaa.verificationPairingSRS_G2 stmt () pairing SRS_elem) * Lipmaa.SRSElementValue_G2 SRS_elem)
                  Lipmaa.ListSRSElements_G2).sum))
        (Lipmaa.ListPairings ())).sum =
    0
i : Fin n_wit
hi : i ∈ Finset.univ
⊢ (Polynomial.X - Polynomial.C (r i)).Monic