Proof with Tarski.
intros.
unfold out in H.
decompose [and] H;clear H.
split.
unfold Col;intuition.
intuition.
assert (A = P).
eTarski.
intuition.
assert (B = P).
assert (Bet B P A);Between.
eTarski.
intuition.
Qed.

(* Specifications: *)
Lemma l6_4_2 : forall A B P,
Col A P B /\ ~ Bet A P B -> out P A B.