def un.le_dbl
import bend-osdev-u32@0.1.0.0/PROOF.bend as PROOFimport Base
160def un.le_dbl(x: Nat, y: Nat) -> {Nat.is_le(Nat.double(x), Nat.double(y)) == Nat.is_le(x, y) : Bool}:
161 match x y:
162 case 0n 0n:
163 {==}
164 case 0n 1n+q:
165 {==}
166 case 1n+p 0n:
167 {==}
168 case 1n+p 1n+q:
169 un.le_dbl(p, q)