law word_adc_exact

bend-mathlib@0.8.1.0 · u32.bend:300

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

300# The adder is exact below the overflow: a + b + carry-in < 2^n implies to_nat (adc a b False c) = a + b + carry-in.
301law word_adc_exact:
302  for n: Nat
303  for a: Word(n)
304  for b: Word(n)
305  for c: Bool
306  for h: MNat.lt(Nat.add(Nat.add(Word.to_nat(n, a), Word.to_nat(n, b)), Bool.pick(Nat, c, 1n, 0n)), Nat.pow(2n, n))
307  {Word.to_nat(n, Word.adc(n, a, b, False{}, c)) == Nat.add(Nat.add(Word.to_nat(n, a), Word.to_nat(n, b)), Bool.pick(Nat, c, 1n, 0n)) : Nat}