proposition: Lemma lea_line : forall A B C P, Bet A B P -> LeA A B P A B C -> Bet A B C.
proof: Proof. intros. unfold LeA in H0. ex_and H0 PP. assert (HH:=H0). unfold InAngle in H0. spliter. ex_and H4 X. induction H5. subst X. assumption. assert (Bet A B PP). eapply bet_conga__bet. apply H. assumption. eapply bet_in_angle_bet. apply H6. assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2