(** 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'.
Lemma l4_6 : forall A B C A' B' C', Bet A B C -> Cong_3 A B C A' B' C' -> Bet A' B' C'.
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.