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

(* Specifications: *)
Lemma power_le : forall x n : nat, 0 < n -> x <= power x n.
Lemma power_mult :
forall x a b : nat, power x a * power x b = power x (a + b).
Lemma power_power : forall x a b : nat, power (power x a) b = power x (a * b).
Lemma SO_power : forall x : nat, power 1 x = 1.
Lemma power_O : forall n : nat, 1 <= n -> power 0 n = 0.
Definition plus_eq := f_equal2 plus.