proposition: Lemma same_dir_to_null : forall A B C D, Same_dir A B C D -> Same_dir A B D C -> A = B /\ C = D.
proof: Proof. intros. assert(Same_dir C D D C). apply (same_dir_trans _ _ A B). apply same_dir_sym. apply H. assumption. apply same_dir_id in H1. subst D. apply same_dir_sym in H. apply same_dir_null in H. subst B. tauto. Qed.
imports: GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec