proposition: Lemma expRat_exp_prod : forall n1 n2 r, expRat r (n1 * n2)%nat == expRat (expRat r n1) n2.
proof: Proof. induction n1; intuition; simpl in *. symmetry. eapply expRat_1. rewrite expRat_exp_sum. rewrite IHn1. rewrite expRat_base_prod. intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms