proposition: Lemma distance_non_nulle : forall A B : PO, scalaire (vec A B) (vec A B) <> 0 -> A <> B :>PO.
proof: Proof. intros; unfold not in |- *; intros. apply H. rewrite H0. replace (vec B B) with (mult_PP 0 (vec A B)). Simplscal. unfold vec in |- *; RingPP. Qed.