ProofCore.add_fits: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_core.bend as ProofCore
Lines 531-538 of lawful-bytes@0.1.1.0/proof_core.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&start_line=531&end_line=538

import Base

# A sum of two words that stays within 4 * 2^d does not wrap.
law add_fits:
  for +a: U32
  for +b: U32
  for +d: Nat
  for +hd: {Nat.is_le(d, 29n) == True{} : Bool}
  for +h: {Nat.is_le(Nat.add(U32.to_nat(a), U32.to_nat(b)), Nat.mul(4n, Nat.pow(2n, d))) == True{} : Bool}
  {U32.to_nat(U32.add(a, b)) == Nat.add(U32.to_nat(a), U32.to_nat(b)) : Nat}

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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=lawful-bytes@0.1.1.0/proof_core.bend&name=fits_e
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=he32
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_add_fits_p