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 between_one : forall A B C,
A <> B -> A <> C -> B <> C -> ColH A B C ->
BetH A B C \/ BetH B C A \/ BetH B A C.