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 eqmod_sign_ext: forall n x, 0 < n < zwordsize -> eqmod (two_p n) (signed (sign_ext n x)) (unsigned x).