split.
intro.
eapply bet_half_bet.
apply H1.
assumption.
assumption.
intro.
eapply bet_double_bet.
apply H.
apply H0.
assumption.
Qed.

Lemma symmetry_preseves_bet1 : forall A B M A' B', Midpoint M A A' -> Midpoint M B B' -> Bet M A B -> Bet M A' B'.
intros.