Laws.Inverse.unit: law of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/laws.bend as Laws
Lines 47-53 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/laws.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/laws.bend&start_line=47&end_line=53

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/aes.bend as S

# The specification's inverse (a^254) is the multiplicative inverse of
# FIPS 197 section 4.4: a * a^-1 = {01} for every nonzero byte, and {00}
# goes to {00} (5.1.1); so S.sbox is "inverse, then affine map".
law Inverse.unit:
  for +x: U32
  for +h: {U32.is_eq(U32.and(255, x), 0) == False{} : Bool}
  {S.mul(x, S.inverse(x)) == 1 : U32}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/inverse.bend&name=inverse_unit
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/aes.bend&name=inverse
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/aes.bend&name=mul