intros p q H'.
case (le_or_lt q p); auto; (intros H'1; generalize H'; case H'1).
intros H'0; Contradict H'0; auto with zarith.
intros m H'0 H'2; Contradict H'2; auto with zarith.
Qed.

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