U32.word_sub_exact_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 1079-1085 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=1079&end_line=1085

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

# Word subtraction is exact without underflow: b <= a implies to_nat (sub a b) = a - b, reversed to rewrite toward the simple side.
law word_sub_exact_sym:
  for n: Nat
  for a: Word(n)
  for b: Word(n)
  for h: MNat.le(Word.to_nat(n, b), Word.to_nat(n, a))
  {Nat.sub(Word.to_nat(n, a), Word.to_nat(n, b)) == Word.to_nat(n, Word.sub(n, a, b)) : Nat}

Uses (8):
  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.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.sub
  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=le
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/u32.bend&name=word_sub_exact