proposition: Lemma col_lta__bet : forall A B C X Y Z, Col X Y Z -> LtA A B C X Y Z -> Bet X Y Z.
proof: Proof. intros. destruct H0. assert (Hd := H0). apply not_out_bet. assumption. intro. apply H1. apply lea_asym. assumption. apply lea_distincts in H0. spliter. apply l11_31_1; auto. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2