def un.bao
import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOFimport Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
1886def un.bao(x: Bool, y: Bool) -> {Nat.add(U.U32Nat.bit(Bool.and(x, y)), U.U32Nat.bit(Bool.or(x, y))) == Nat.add(U.U32Nat.bit(x), U.U32Nat.bit(y)) : Nat}:
1887 match x y:
1888 case True{} True{}:
1889 {==}
1890 case True{} False{}:
1891 {==}
1892 case False{} True{}:
1893 {==}
1894 case False{} False{}:
1895 {==}