Inverse.cong_mul_r: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend as Inverse
Lines 35-37 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend&start_line=35&end_line=37

import Base
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as R

def 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}:
  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)),
    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)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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/math/natural/arith.bend&name=mod_mul_r