proposition: Lemma ltps__ltp: forall O E E' A B, LtPs O E E' A B -> LtP O E E' A B.
proof: Proof. intros. unfold LtPs in H. ex_and H D. unfold LtP. exists D. split; auto. apply sum_diff. assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch14_order