Proof with Tarski.
intros.
unfold Col in *.
elim H1;intro;elim H2;intro.
right.
assert (Bet P S X \/ Bet P X S).
apply (l5_2 Q P S X);Between;intuition;Between...
intuition;Between...
elim H4;intro.
left;Between.
left;Between.
elim H3;intro.
left;Between.
left;Between.
elim H3;intro.
elim H4;intro.
right.
assert (Bet P S X \/ Bet P X S).
apply (l5_1 P Q S X);Between.
intuition;Between.
right;right;Between.
elim H4;intro.
right;left;Between.
right.
assert (Bet P S X \/ Bet P X S).
apply (l5_3 P S X Q);intuition;Between.
intuition;Between.
Qed.

(* Specifications: *)
Lemma l6_16_2 : forall P Q S X,
P<>Q -> S<>P -> Col S P Q -> (Col X P S -> Col X P Q).