Xbits.xor_bits: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend as Xbits
Lines 174-196 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&start_line=174&end_line=196

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/x25519.bend as S
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

# swap ^= k_t on bits
def xor_bits(+a: U32, +b: U32, +na: Nat, +nb: Nat, +ea: {v(a) == na : Nat}, +eb: {v(b) == nb : Nat}, +ha: {Nat.is_le(na, 1n) == True{} : Bool}, +hb: {Nat.is_le(nb, 1n) == True{} : Bool}) -> {v(U32.xor(a, b)) == S.bxor(na, nb) : Nat}:
  match na nb:
    case 0n 0n:
      %Equal.sym(U32, a, 0, u0(a, ea)) : {v(U32.xor(_, b)) == 0n : Nat}
      %Equal.sym(U32, b, 0, u0(b, eb)) : {v(U32.xor(0, _)) == 0n : Nat}
      {==}
    case 0n 1n:
      %Equal.sym(U32, a, 0, u0(a, ea)) : {v(U32.xor(_, b)) == 1n : Nat}
      %Equal.sym(U32, b, 1, u1(b, eb)) : {v(U32.xor(0, _)) == 1n : Nat}
      {==}
    case 1n 0n:
      %Equal.sym(U32, a, 1, u1(a, ea)) : {v(U32.xor(_, b)) == 1n : Nat}
      %Equal.sym(U32, b, 0, u0(b, eb)) : {v(U32.xor(1, _)) == 1n : Nat}
      {==}
    case 1n 1n:
      %Equal.sym(U32, a, 1, u1(a, ea)) : {v(U32.xor(_, b)) == 0n : Nat}
      %Equal.sym(U32, b, 1, u1(b, eb)) : {v(U32.xor(1, _)) == 0n : Nat}
      {==}
    case 2n+q _:
      Empty.absurd({v(U32.xor(a, b)) == S.bxor(2n+q, nb) : Nat}, L.false_true(ha))
    case _ 2n+q:
      Empty.absurd({v(U32.xor(a, b)) == S.bxor(na, 2n+q) : Nat}, L.false_true(hb))

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=Empty.absurd
  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=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.xor
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=u0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=u1
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/xbits.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/x25519.bend&name=bxor