def bitw.ctz_clz.h
import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOFimport Base
512def bitw.ctz_clz.h(+k: Nat, +m: Nat, l: Nat, e: {Nat.is_le(1n+k, l) == True{} : Bool}, f: {Nat.is_le(l, 1n+m) == True{} : Bool}) -> {Nat.is_le(Nat.add(k, Nat.sub(1n+m, l)), m) == True{} : Bool}:
513 match l:
514 case 0n:
515 Empty.absurd({Nat.is_le(Nat.add(k, 1n+m), m) == True{} : Bool}, absurd.ft(e))
516 case 1n+i:
517 nat.add_sub_le(k, i, m, e, f)