U32.word_inc_exact: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 401-406 of bend-mathlib@0.8.1.0/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/u32.bend&start_line=401&end_line=406

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

# Increment is exact without overflow: 1 + w < 2^n implies to_nat (inc w) = 1 + w.
law word_inc_exact:
  for n: Nat
  for w: Word(n)
  for h: MNat.lt(1n+Word.to_nat(n, w), Nat.pow(2n, n))
  {Word.to_nat(n, Word.inc(n, w)) == 1n+Word.to_nat(n, w) : Nat}

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.inc
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_fin_exact
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_inc_carry
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=internal_inc_core