Arith.mod_mul_l: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as Arith
Lines 162-165 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&start_line=162&end_line=165

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

def 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}:
  %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}
  %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}
  mod_mul_r(bp, y, x)

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=mod_mul_r