PROOF.un.bxa: def of bend-osdev-u32@0.1.0.0
Import: import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOF
Lines 1897-1906 of bend-osdev-u32@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-u32@0.1.0.0/PROOF.bend&start_line=1897&end_line=1906

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U

def un.bxa(x: Bool, y: Bool) -> {Nat.add(U.U32Nat.bit(Bool.xor(x, y)), Nat.double(U.U32Nat.bit(Bool.and(x, y)))) == Nat.add(U.U32Nat.bit(x), U.U32Nat.bit(y)) : Nat}:
  match x y:
    case True{} True{}:
      {==}
    case True{} False{}:
      {==}
    case False{} True{}:
      {==}
    case False{} False{}:
      {==}

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=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.xor
  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=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.bit