def un.low_zero
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
1265def un.low_zero(k: Nat) -> {U.U32Nat.low(k, 0n) == 0n : Nat}:
1266 match k:
1267 case 0n:
1268 {==}
1269 case 1n+ +j:
1270 un.double_cong(U.U32Nat.low(j, 0n), 0n, un.low_zero(j))