intros p q H'; elim H'; simpl in |- *; auto.
apply Zpower_nat_monotone_S.
intros m H H0; apply Zlt_trans with (1 := H0).
apply Zpower_nat_monotone_S.
Qed.
Hint Resolve Zpower_nat_monotone_lt: zarith.

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