def ns.half_lt
import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShiftimport Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
171def ns.half_lt(x: Nat) -> {Nat.is_lt(x, 2n+Nat.double(U.U32Nat.half(x))) == True{} : Bool}:
172 match x:
173 case 0n:
174 {==}
175 case 1n+ +p:
176 match p:
177 case 0n:
178 {==}
179 case 1n+ +q:
180 ns.half_lt(q)