Proof with Tarski.
intros.
assert (exists C, Bet A P C /\ P<>C)...
DecompExAnd H0 C.
assert (Bet B P C <-> out P A B).
eapply l6_2;unfold out in H;intuition.
repeat split.
unfold out in H;intuition.
unfold out in H;intuition.
exists C;repeat split;eauto.
intuition.
Qed.

(* Specifications: *)
Lemma l6_3_2 : forall A B P,
(A<>P /\ B<>P /\ exists C, C<>P /\ Bet A P C /\ Bet B P C) -> out P A B.