Proof with Tarski.
unfold FSC.
intros.
intuition.
unfold Col in H1.
intuition.
assert (Bet A' B' C').
eapply l4_6; try apply H3;unfold Cong_3 in *;intuition...
unfold Cong_3 in H;intuition.
assert (A<>B);auto.
eapply five_segments;try apply H5;auto.
assert (Bet B' C' A').
apply (l4_6 B C A B' C' A')...
unfold Cong_3 in *;intuition.
unfold Cong_3 in H;intuition.
assert (IFSC A C B D A' C' B' D').
unfold IFSC;intuition.
eapply l4_2.
apply H6.
assert (Bet C' A' B').
apply (l4_6 C A B C' A' B')...
unfold Cong_3 in *;intuition.
unfold Cong_3 in H;intuition.
eapply five_segments.
2:apply H.
3:assumption.
3:apply between_symmetry;apply H1.
3:apply between_symmetry;apply H3.
sTarski.
sTarski.
auto.
Qed.

Lemma l4_17 :  forall A B C P Q,
A<>B -> Col A B C ->
Cong A P A Q  -> Cong B P B Q -> Cong C P C Q.