def mod_mul_l

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/arith.bend:162

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

162def mod_mul_l(+bp: Nat, +x: Nat, +y: Nat) -> {Nat.mod(Nat.mul(Nat.mod(x, 1n+bp), y), 1n+bp) == Nat.mod(Nat.mul(x, y), 1n+bp) : Nat}:
163  %Equal.sym(Nat, Nat.mul(Nat.mod(x, 1n+bp), y), Nat.mul(y, Nat.mod(x, 1n+bp)), A.mul_comm(Nat.mod(x, 1n+bp), y)) : {Nat.mod(_, 1n+bp) == Nat.mod(Nat.mul(x, y), 1n+bp) : Nat}
164  %Equal.sym(Nat, Nat.mul(x, y), Nat.mul(y, x), A.mul_comm(x, y)) : {Nat.mod(Nat.mul(y, Nat.mod(x, 1n+bp)), 1n+bp) == Nat.mod(_, 1n+bp) : Nat}
165  mod_mul_r(bp, y, x)