ProofU32.wshl.m: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_u32.bend as ProofU32
Lines 63-67 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=63&end_line=67

import Base
import lawful-words@0.1.0.0/proof_nat.bend as N
import lawful-words@0.1.0.0/proof_word.bend as W

law wshl.m:
  for +w: Word(32n)
  for +m: Nat
  for +hm: {Nat.pow(2n, 32n) == m : Nat}
  {Nat.add(Word.to_nat(32n, Word.shl(32n, w)), Nat.mul(N.bn(W.shtop(32n, w)), m)) == Nat.double(Word.to_nat(32n, w)) : Nat}

Uses (11):
  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.double
  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.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=bn
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=shtop
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_word.bend&name=wshl