unfold disjoint.
intro.
destruct H0 as [P []].
assert(HP:= betH_trans0 A P B C H0 H).
spliter.
apply between_only_one' in H1.
spliter.
contradiction.
Qed.

Lemma betH2_out : forall A B C D, B <> C -> BetH A B D -> BetH A C D -> BetH A B C \/ BetH A C B.