ProofFastWord.p0_xor: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_word.bend as ProofFastWord
Lines 111-116 of lawful-bytes@0.1.1.0/proof_fast_word.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&start_line=111&end_line=116

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/fast.bend as FA
import lawful-bytes@0.1.1.0/proof_core.bend as C

# Searching w for c is searching w xor rep(c) for a zero byte.
law p0_xor:
  for +w: U32
  for +c: U32
  for +hc: {U32.is_lt(c, 256) == True{} : Bool}
  {P0(U32.xor(w, FA.rep(c))) == D.run_len(C.L4(w), c) : Nat}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.xor
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=run_len
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=rep
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=L4
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_w2.bend&name=R4
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_w2.bend&name=ej_xor
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&name=P0
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=byte