def uq.half_dbl
import bend-osdev-algo@0.1.0.0/proof_u32.bend as ProofU32import Base
521def uq.half_dbl(x: Nat) -> {uq.half(Nat.double(x)) == x : Nat}:
522 match x:
523 case 0n:
524 {==}
525 case 1n+p:
526 uq.succ_cong(uq.half(Nat.double(p)), p, uq.half_dbl(p))