ProofNat.mod_add_mul: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_nat.bend as ProofNat
Lines 1175-1180 of lawful-words@0.1.0.0/proof_nat.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_nat.bend&start_line=1175&end_line=1180

import Base

# Adding a multiple of x does not change the remainder by x.
law mod_add_mul:
  for +j: Nat
  for +x: Nat
  for +z: Nat
  {Nat.mod(Nat.add(Nat.mul(j, x), z), x) == Nat.mod(z, x) : Nat}

Uses (14):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  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=lawful-words@0.1.0.0/proof_nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=div_mod
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mod_mul_add
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_add_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_zero_r