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

Lemma Zshiftin_ind:
forall (P: Z -> Prop),
P 0 ->
(forall b x, 0 <= x -> P x -> P (Zshiftin b x)) ->
forall x, 0 <= x -> P x.