simpl in |- *; auto with arith.
intros.
simpl in |- *.
apply lt_nm_mult; auto with arith.
Qed.
Hint Resolve exp_n_pos.

(* Specifications: *)
Lemma le_exp_n_mult : forall n p : nat, 0 < n -> exp_n n p <= n * exp_n n p.
auto with arith.