proposition: Lemma plgs_diff : forall A B C D, Parallelogram_strict A B C D -> Parallelogram_strict A B C D /\ A <> B /\ B <> C /\ C <> D /\ D <> A /\ A <> C /\ B <> D.
proof: Proof. intros. split. assumption. unfold Parallelogram_strict in H. spliter. unfold TS in H. spliter. repeat split; intro. subst B. apply H. Col. subst C. apply H. Col. subst D. apply H2. Col. subst D. apply H2. Col. subst C. apply H. Col. subst D. ex_and H3 T. apply between_identity in H4. subst T. contradiction. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel