proposition: Lemma col_cong2_bet3 : forall A B C D, Col A B D -> Bet A B C -> Cong A B C D -> Cong A C B D -> Bet B C D.
proof: Proof. intros. induction(eq_dec_points A B). subst B. apply cong_symmetry in H1. apply cong_identity in H1. subst D. Between. eapply (col_cong2_bet2 _ A). apply bet_col in H0. ColR. Between. Cong. Cong. Qed.
imports: GeoCoq.Tarski_dev.Ch06_out_lines GeoCoq.Tarski_dev.Tactics.ColR