law u32_add_exact_sym

bend-mathlib@0.8.1.0 · u32.bend:1163

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

1163# U32 addition is exact without overflow: a + b < 2^32 implies to_nat (a + b) = a + b, reversed to rewrite toward the simple side.
1164law u32_add_exact_sym:
1165  for a: U32
1166  for b: U32
1167  for h: MNat.lt(Nat.add(U32.to_nat(a), U32.to_nat(b)), Nat.pow(2n, 32n))
1168  {Nat.add(U32.to_nat(a), U32.to_nat(b)) == U32.to_nat(U32.add(a, b)) : Nat}