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 sign_ext_shr_shl: forall n x, 0 < n < zwordsize -> let y := repr (zwordsize - n) in sign_ext n x = shr (shl x y) y.