Corollary Ztestbit_two_p_m1:
  forall n i, 0 <= n -> 0 <= i ->
  Z.testbit (two_p n - 1) i = if zlt i n then true else false.

Lemma Ziter_succ: forall (A: Type) n (f: A -> A) x, 0 <= n -> Z.iter (Z.succ n) f x = f (Z.iter n f x).