eapply l7_15.
apply l7_3_2.
apply l7_2.
apply H.
apply l7_2.
apply H0.
assumption.
Qed.

Lemma symmetry_preserves_bet : forall A B M A' B', Midpoint M A A' -> Midpoint M B B' -> (Bet M A' B' <-> Bet M A B).
intros.