U32.u32_add_exact_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/u32.bend as U32
Lines 1163-1168 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=1163&end_line=1168

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

# U32 addition is exact without overflow: a + b < 2^32 implies to_nat (a + b) = a + b, reversed to rewrite toward the simple side.
law u32_add_exact_sym:
  for a: U32
  for b: U32
  for h: MNat.lt(Nat.add(U32.to_nat(a), U32.to_nat(b)), Nat.pow(2n, 32n))
  {Nat.add(U32.to_nat(a), U32.to_nat(b)) == U32.to_nat(U32.add(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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.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=u32_add_exact