induction m;simpl;auto with arith.
rewrite IHm;ring.
rewrite power_mult_lemma1;rewrite IHn;rewrite <- power_plus_lemma1;trivial.
Qed.

(* Specifications: *)
Lemma power_zero : forall (n x:nat),(power x n)=O->x=O.
induction n;simpl;intros.