ProofU32.wmul.m: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_u32.bend as ProofU32
Lines 86-92 of lawful-words@0.1.0.0/proof_u32.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_u32.bend&start_line=86&end_line=92

import Base

law wmul.m:
  for +x: Word(32n)
  for +y: Word(32n)
  for +m: Nat
  for +hm: {Nat.pow(2n, 32n) == m : Nat}
  {Word.to_nat(32n, Word.mul.go(32n, 32n, x, y, Word.zero(32n)))
    == Nat.mod(Nat.add(Word.to_nat(32n, Word.zero(32n)), Nat.mul(Word.to_nat(32n, x), Word.to_nat(32n, y))), m) : Nat}

Uses (10):
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.mul.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=wmul_go