Hint Resolve between_inner_transitivity : Tarski.
Hint Resolve between_exchange2 between_exchange3 between_exchange4 : Tarski.
Hint Resolve outer_transitivity_between outer_transitivity_between2 : Tarski.
Hint Resolve between_inner_transitivity
between_exchange2 between_exchange3 between_exchange4
outer_transitivity_between outer_transitivity_between2
between_symmetry : Between.
Ltac Between := eauto with Between.
(* Axiom 20.1 of Givant Lemma unique_triangle : forall A B C C' D, A <> B -> Cong A C A C' -> Cong B C B C' -> Bet B D C' -> (Bet A D C \/ Bet A C D) -> C=C'. Axiom 21 of Givant Lemma existence_triangle : forall A B A' B' C', Cong A B A' B' -> exists C X, Cong A C A' C' /\ Cong B C B' C' /\ Bet C X P /\ Col A B X. *)
(** We formalize $Bet_n$ only for n=4. *)
Definition Bet_4 := fun A1 A2 A3 A4 =>
Bet A1 A2 A3 /\ Bet A2 A3 A4 /\ Bet A1 A3 A4 /\ Bet A1 A2 A4.

(* Specifications: *)
Lemma l_3_9_4 : forall A1 A2 A3 A4,
Bet_4 A1 A2 A3 A4 -> Bet_4 A4 A3 A2 A1.