rewrite <- two_power_nat_correct. rewrite two_power_nat_S. rewrite two_power_nat_correct.
omega. Qed.

Lemma Zpower_nat_Zpower : forall i : nat, Zpower_nat 2 i = 2 ^ Z_of_nat i.
induction i. simpl. trivial. rewrite <- two_power_nat_correct. rewrite two_power_nat_S.