U32.word_add_exact_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 1039-1045 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=1039&end_line=1045

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

# Word addition is exact without overflow: a + b < 2^n implies to_nat (add a b) = a + b, reversed to rewrite toward the simple side.
law word_add_exact_sym:
  for n: Nat
  for a: Word(n)
  for b: Word(n)
  for h: MNat.lt(Nat.add(Word.to_nat(n, a), Word.to_nat(n, b)), Nat.pow(2n, n))
  {Nat.add(Word.to_nat(n, a), Word.to_nat(n, b)) == Word.to_nat(n, Word.add(n, a, b)) : Nat}

Uses (9):
  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.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.add
  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=word_add_exact