proposition: Lemma inv_nexp_even : forall (x : R) n, Nat.Even n -> [--]x[^]n [=] x[^]n.
proof: Proof. intros x n [k H]. replace (2 * k) with (k + k) in H by lia; rewrite H. astepl ( [--]x[^](k)[*] [--]x[^](k)). astepl (( [--]x[*] [--]x) [^](k)). astepl ((x[*]x) [^](k)). Step_final (x[^](k)[*]x[^](k)). 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)