proposition: Lemma mid__lt : forall A M B, A <> B -> Midpoint M A B -> Lt A M A B.
proof: Proof. intros A M B HAB HM. destruct (midpoint_distinct_1 M A B HAB HM) as [HMA HMB]. destruct HM. split. exists M; Cong. intro. apply HMB, between_cong with A; auto. Qed.
imports: GeoCoq.Tarski_dev.Ch06_out_lines GeoCoq.Tarski_dev.Tactics.ColR