def cong_mul_r
bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/inverse.bend:35
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/inverse.bend as Inverse
import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/arith.bend as R
35def cong_mul_r(+mp: Nat, +x: Nat, +y: Nat, +y2: Nat, +e: {Nat.mod(y, 1n+mp) == Nat.mod(y2, 1n+mp) : Nat}) -> {Nat.mod(Nat.mul(x, y), 1n+mp) == Nat.mod(Nat.mul(x, y2), 1n+mp) : Nat}:
36 Equal.trans(Nat, Nat.mod(Nat.mul(x, y), 1n+mp), Nat.mod(Nat.mul(x, Nat.mod(y, 1n+mp)), 1n+mp), Nat.mod(Nat.mul(x, y2), 1n+mp), Equal.sym(Nat, Nat.mod(Nat.mul(x, Nat.mod(y, 1n+mp)), 1n+mp), Nat.mod(Nat.mul(x, y), 1n+mp), R.mod_mul_r(mp, x, y)),
37 Equal.trans(Nat, Nat.mod(Nat.mul(x, Nat.mod(y, 1n+mp)), 1n+mp), Nat.mod(Nat.mul(x, Nat.mod(y2, 1n+mp)), 1n+mp), Nat.mod(Nat.mul(x, y2), 1n+mp), Equal.cong(Nat, Nat, z => Nat.mod(Nat.mul(x, z), 1n+mp), Nat.mod(y, 1n+mp), Nat.mod(y2, 1n+mp), e), R.mod_mul_r(mp, x, y2)))