Proof with Tarski.
intros.
unfold iff;split;intro.
unfold out;repeat split;auto.
eapply l5_2;eauto;sTarski.
unfold out in H3.
decompose [and] H3.
elim H7;intro;Between.
Qed.

Lemma l6_3_1 : forall A B P,
out P A B -> (A<>P /\ B<>P /\ exists C, C<>P /\ Bet A P C /\ Bet B P C).