proposition: Lemma zmult_wd : forall (x y:G) (n m:Z), (x [=] y) -> n = m -> zmult x n [=] zmult y m.
proof: Proof. do 3 intro. case n; intros; inversion H0. algebra. unfold zmult in |- *. simpl in |- *. astepl (nmult x (nat_of_P p)); Step_final (nmult y (nat_of_P p)). simpl in |- *. astepl [--](nmult x (nat_of_P p)). Step_final [--](nmult y (nat_of_P p)). Qed.
imports: CoRN.algebra.CGroups