proposition: Lemma x_plus_x : forall (R : CRing) (x : R), x[+]x [=] Two[*]x.
proof: Proof. intros R x. astepl ([1][*]x[+][1][*]x). astepl (([1][+][1]) [*]x). simpl in |- *; algebra. 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)