proposition: Lemma dist_2a : forall x y z : R, z[*] (x[-]y) [=] z[*]x[-]z[*]y.
proof: Proof. intros x y z. astepl (z[*] (x[+] [--]y)). astepl (z[*]x[+]z[*] [--]y). Step_final (z[*]x[+] [--] (z[*]y)). 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)