Lemmas.word_inc_nat: law of bend-kit-lemmas@0.1.1.0
Import: import bend-kit-lemmas@0.1.1.0/lemmas.bend as Lemmas
Lines 656-661 of bend-kit-lemmas@0.1.1.0/lemmas.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-lemmas@0.1.1.0/lemmas.bend&start_line=656&end_line=661

import Base
import bend-mathlib@0.7.4.0/nat.bend as MNat

# Incrementing without overflow adds one.
law word_inc_nat:
  for n: Nat
  for w: Word(n)
  for h: MNat.lt(1n+Word.to_nat(n, w), pow2(n))
  {Word.to_nat(n, Word.inc(n, w)) == 1n+Word.to_nat(n, w) : Nat}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  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-kit-lemmas@0.1.1.0/lemmas.bend&name=lt_of_double_lt
  https://jend.leeeet.dev/definition.txt?path=bend-kit-lemmas@0.1.1.0/lemmas.bend&name=pow2
  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/nat.bend&name=lt_irrefl