proposition: Theorem expnat_exp_le : forall n2 n4 n, (n2 > 0 \/ n > 0) -> n2 <= n4 -> expnat n n2 <= expnat n n4.
proof: Proof. induction n2; destruct n4; simpl in *; intuition; try lia. rewrite <- Nat.mul_1_l at 1. eapply Nat.mul_le_mono. lia. eapply expnat_ge_1; trivial. destruct (eq_nat_dec n 0); subst. simpl; intuition. eapply Nat.mul_le_mono; intuition. eapply IHn2. lia. lia. Qed.
imports: Arith micromega.Lia Coq.NArith.BinNat