intros p; rewrite <- (Zmult_1_l (Zpower_nat n p)); replace (S p) with (1 + p);
[ rewrite Zpower_nat_is_exp | auto with zarith ].
rewrite Zpower_nat_1; auto with zarith.
apply Zmult_gt_0_lt_compat_r; auto with zarith.
apply Zlt_gt; auto with zarith.
Qed.

(* Specifications: *)
Theorem Zpower_nat_monotone_lt :
forall p q : nat, p < q -> (Zpower_nat n p < Zpower_nat n q)%Z.