proposition: Lemma one_nexp : forall n : nat, ([1]:R) [^]n [=] [1].
proof: Proof. intro n. induction n as [| n Hrecn]. algebra. astepl (([1]:R) [*][1][^]n). Step_final (([1]:R) [*][1]). Qed.
imports: CoRN.tactics.CornTac CoRN.algebra.CSums CoRN.algebra.CAbMonoids Coq.Sorting.Permutation CoRN.util.SetoidPermutation Coq.Setoids.Setoid Coq.Classes.Morphisms Coq(Lia)