Proof with Tarski.
intros.
unfold out.
intuition.
subst A.
assert (Bet P P B)...
subst B.
assert (Bet A P P)...
unfold Col in H0;intuition.
Qed.
(** out reflexivity. *)

(** out transitivity. *)
Lemma l6_7 : forall P A B C, out P A B -> out P B C -> out P A C.