intros.
assert
(exists x : Point,
Bet B x B /\ Bet A x A).
eapply inner_pasch;eauto.
DecompExAnd H1 x.
assert (A = x)...
assert (B = x)...
rewrite <- H2 in H1.
assumption.
Qed.
Hint Resolve between_egality : Tarski.
(** Inner transitivity 'axiom' for betweenness. *)

Lemma between_inner_transitivity : forall A B C D,
Bet A B D -> Bet B C D -> Bet A B C.