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 betH_dec : forall A B C, A <> B -> B <> C -> A <> C -> BetH A B C \/ ~ BetH A B C.