ProofWord.adc_step: law of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_word.bend as ProofWord
Lines 365-380 of lawful-words@0.1.0.0/proof_word.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_word.bend&start_line=365&end_line=380

import Base

# One bit of the sum, as numbers.
law adc_step:
  for +p: Nat
  for +x: Nat
  for +y: Nat
  for +c: Nat
  for +s: Nat
  for +k: Nat
  for +a: Nat
  for +b: Nat
  for +r: Nat
  for +co: Nat
  for +ih: {Nat.add(r, Nat.mul(co, Nat.pow(2n, p))) == Nat.add(k, Nat.add(a, b)) : Nat}
  for +bit: {Nat.add(s, Nat.double(k)) == Nat.add(c, Nat.add(x, y)) : Nat}
  {Nat.add(Nat.add(s, Nat.double(r)), Nat.mul(co, Nat.pow(2n, 1n+p)))
    == Nat.add(c, Nat.add(Nat.add(x, Nat.double(a)), Nat.add(y, Nat.double(b)))) : Nat}

Uses (11):
  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.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=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=add_swap
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=dbl_dist
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=mul_dbl_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=pow2s