def bq.half_le
import bend-osdev-algo@0.1.0.0/proof_bsearch.bend as ProofBsearchimport Base
import bend-osdev-algo@0.1.0.0/proof_u32.bend as U
339def bq.half_le(q: Nat) -> {Nat.is_le(U.uq.half(q), q) == True{} : Bool}:
340 match q:
341 case 0n:
342 {==}
343 case 1n+p:
344 match p:
345 case 0n:
346 {==}
347 case 1n+ +r:
348 bq.le_succ_r(U.uq.half(r), r, bq.half_le(r))