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.

Theorem modu_and: forall x n logn, is_power2 n = Some logn -> modu x n = and x (sub n one).