destruct m;simpl;try omega.
simpl in IHm.
assert (1 < p*(power p m)).
apply IHm;auto with arith.
rewrite mult_comm.
apply lt_trans with (1*p);try omega.
apply mult_lt_compat_r;try omega.
Qed.

(** 1^n = 1 *)
Lemma power_one : forall (n:nat),(power 1 n)=1.
induction n;simpl;trivial.