Gf.tx_xor: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend as Gf
Lines 202-206 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&start_line=202&end_line=206

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

def tx_xor(+n: Nat, +low: Word(n), +a: Word(n), +b: Word(n)) -> {P.times_x(n, low, Word.xor(n, a, b)) == Word.xor(n, P.times_x(n, low, a), P.times_x(n, low, b)) : Word(n)}:
  %Equal.sym(Bool, P.top(n, Word.xor(n, a, b)), Bool.xor(P.top(n, a), P.top(n, b)), top_xor(n, a, b)) : {Word.xor(n, P.wscale(n, _, low), Word.shl(n, Word.xor(n, a, b))) == Word.xor(n, P.times_x(n, low, a), P.times_x(n, low, b)) : Word(n)}
  %Equal.sym(Word(n), P.wscale(n, Bool.xor(P.top(n, a), P.top(n, b)), low), Word.xor(n, P.wscale(n, P.top(n, a), low), P.wscale(n, P.top(n, b), low)), wscale_xor(n, P.top(n, a), P.top(n, b), low)) : {Word.xor(n, _, Word.shl(n, Word.xor(n, a, b))) == Word.xor(n, P.times_x(n, low, a), P.times_x(n, low, b)) : Word(n)}
  %Equal.sym(Word(n), Word.shl(n, Word.xor(n, a, b)), Word.xor(n, Word.shl(n, a), Word.shl(n, b)), shl_xor(n, a, b)) : {Word.xor(n, Word.xor(n, P.wscale(n, P.top(n, a), low), P.wscale(n, P.top(n, b), low)), _) == Word.xor(n, P.times_x(n, low, a), P.times_x(n, low, b)) : Word(n)}
  xor_swap4(n, P.wscale(n, P.top(n, a), low), P.wscale(n, P.top(n, b), low), Word.shl(n, a), Word.shl(n, b))

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.xor
  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=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.shl
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.xor
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=shl_xor
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=top_xor
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=wscale_xor
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/aes/gf.bend&name=xor_swap4
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend&name=times_x
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend&name=top
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/aes/poly.bend&name=wscale