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 Zquot_Zdiv: forall x y, y > 0 -> Z.quot x y = if zlt x 0 then (x + y - 1) / y else x / y.