Proof with Between.
intros.
assert (Bet A C D \/ Bet A D C).
eapply l5_1;try apply H...
intuition...
Qed.
(** Inner connectivity axiom for betweenness *)
(** Axiom 17 of Givant *)

Lemma l5_3 : forall A B C D,
Bet A B D -> Bet A C D -> Bet A B C \/ Bet A C B.