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

Lemma Ztestbit_le:
forall x y,
0 <= y ->
(forall i, 0 <= i -> Z.testbit x i = true -> Z.testbit y i = true) ->
x <= y.