proposition: Lemma col_cong2_bet4 : forall A B C D, Col A B C -> Bet A B D -> Cong A B C D -> Cong A D B C -> Bet B D C.
proof: Proof. intros. induction(eq_dec_points A B). subst B. apply cong_symmetry in H1. apply cong_identity in H1. subst D. Between. apply (col_cong2_bet1 A D B C). apply bet_col in H0. ColR. assumption. Cong. Cong. Qed.
imports: GeoCoq.Tarski_dev.Ch06_out_lines GeoCoq.Tarski_dev.Tactics.ColR