intros n0; case x; intros.
simpl in |- *; auto.
change (0 * 0 < S n1 * power (S n1) n0) in |- *.
apply lt_mult_right; auto.
Qed.

Lemma power_O : forall n : nat, 1 <= n -> power 0 n = 0.
Definition plus_eq := f_equal2 plus.