proposition: Lemma milieu_parallelogrammme : forall A B C D I : PO, vec A B = vec D C -> I = milieu A C -> I = milieu B D.
proof: Proof. unfold vec in |- *; intros. elim cons_inj with (a := 2) (b := 2) (A := I) (B := milieu B D); intros; auto; try discrR. rewrite <- add_PP_milieu. rewrite H0. rewrite <- add_PP_milieu. RingPP2 H. RingPP. Qed.