proposition: Lemma plg_opp_dir : forall A B C D, Parallelogram A B C D -> Same_dir A B D C.
proof: Proof. intros. induction(eq_dec_points A B). subst B. induction H. apply False_ind. apply plgs_sym in H. apply H. Col. apply plgf_trivial_neq in H. spliter. subst D. left. tauto. unfold Same_dir. right. exists C. split. apply out_trivial. intro. subst D. induction H. apply H. Col. apply plgf_sym in H. apply plgf_trivial_neq in H. tauto. unfold EqV. left. assumption. Qed.
imports: GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec