Proof with Tarski.
intros.
assert (IFSC A B C A A' B' C' A').
unfold IFSC;intuition.
apply cong_commutativity.
eapply l4_2.
apply H3.
Qed.
Hint Resolve l4_2 l4_3 : Tarski.
(** A generalization of the Cong predicate for three points. *)
Definition Cong_3 := fun A1 A2 A3 B1 B2 B3 =>
Cong A1 A2 B1 B2 /\ Cong A1 A3 B1 B3 /\ Cong A2 A3 B2 B3.

(* Specifications: *)
Lemma l4_5 : forall A B C A' C',
Bet A B C -> Cong A C A' C' ->
exists B', Bet A' B' C' /\ Cong_3 A B C A' B' C'.