def cong_mul

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/num.bend:22

import Base

22def cong_mul(+a: Nat, +b: Nat, +c: Nat, +d: Nat, +e1: {a == b : Nat}, +e2: {c == d : Nat}) -> {Nat.mul(a, c) == Nat.mul(b, d) : Nat}:
23  Equal.trans(Nat, Nat.mul(a, c), Nat.mul(b, c), Nat.mul(b, d), Equal.cong(Nat, Nat, t => Nat.mul(t, c), a, b, e1), Equal.cong(Nat, Nat, t => Nat.mul(b, t), c, d, e2))