proposition: Lemma L3 : forall x, dominates_from x (F_ 2) exp2 -> forall k, 0 < k -> dominates_from x (iterate (F_ 2) k) (iterate exp2 k).
proof: Proof. intros x Hx. intros; apply iterate_dom_prop; auto. red;intros. intros i Hi. unfold id_nat. clear Hi. induction i. cbn;auto with arith. cbn. generalize IHi; generalize (exp2 i). intros; lia. apply exp2_mono. destruct (big_induction 2). destruct p;auto. Qed.
imports: Coq(ArithRing Lia Arith)