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 same_side_prime_refl: forall A B C,
~ ColH A B C ->  same_side' C C A B.