Proof with Tarski.
intros.
assert (exists B'', Bet A' B'' C' /\ Cong_3 A B C A' B'' C').
eapply l4_5...
unfold Cong_3 in H0;intuition...
DecompExAnd H1 B''.
assert (Cong_3 A' B'' C' A' B' C').
unfold Cong_3 in *;intuition;esTarski.
assert (IFSC A' B'' C' B'' A' B'' C' B');unfold IFSC;intuition.
unfold Cong_3 in *;intuition...
unfold Cong_3 in *;intuition...
assert (Cong B'' B'' B'' B').
eapply l4_2;eauto.
treat_equalities...
Qed.
Hint Unfold Col.
(** Permutation lemmas for Col *)

(* Specifications: *)
Lemma col_permutation_1 : forall A B C,
Col A B C -> Col B C A.
Lemma col_permutation_2 : forall A B C,
Col A B C -> Col C A B.
Lemma col_permutation_3 : forall A B C,
Col A B C -> Col C B A.
Lemma col_permutation_4 : forall A B C,
Col A B C -> Col B A C.
Lemma col_permutation_5 : forall A B C,
Col A B C -> Col A C B.