ProofFastW1.zbk_byte: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_w1.bend as ProofFastW1
Lines 62-72 of lawful-bytes@0.1.1.0/proof_fast_w1.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_w1.bend&start_line=62&end_line=72

import Base
import lawful-words@0.1.0.0/proof_zb.bend as Z

# With no borrow in and the byte's flag kept by the mask, the masked flags are
# all clear exactly when the byte is not zero and the rest are clear.
law zbk_byte:
  for +n: Nat
  for +x: Word(8n)
  for +r: Word(n)
  for +kr: Word(n)
  for +hr: Word(n)
  for +mr: Word(n)
  {Z.allz(Nat.add(8n, n), Word.and(Nat.add(8n, n), Z.zf(Nat.add(8n, n), Z.app8(n, x, r), Z.app8(n, Z.one8(), kr), Z.app8(n, Z.h8(), hr), True{}), Z.app8(n, Z.h8(), mr)))
    == Bool.and(Bool.not(Z.allz(8n, x)), Z.allz(n, Word.and(n, Z.zf(n, r, kr, hr, True{}), mr))) : Bool}

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=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.not
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Con
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.Nil
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.and
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_zb.bend&name=allz
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_zb.bend&name=app8
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_zb.bend&name=h8
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_zb.bend&name=one8
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_zb.bend&name=zf