Proof with Tarski.
intros.
unfold out;repeat split.
intuition.
intuition.
decompose [and] H.
DecompExAnd H3 C.
eapply l5_2;try apply H4;sTarski.
Qed.

(* Specifications: *)
Lemma l6_4_1 : forall A B P,
out P A B -> Col A P B /\ ~ Bet A P B.