(** 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.

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'.