Proof (same_bits_eqmod wordsize).
Remark two_power_nat_infinity:
forall x, 0 <= x -> exists n, x < two_power_nat n.

Lemma Zsign_bit:
forall n x,
0 <= x < two_power_nat (S n) ->
Z.testbit x (Z.of_nat n) = if zlt x (two_power_nat n) then false else true.