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 cut2_not_cut : forall A B C l, ~ColH A B C -> cut l A B -> cut l A C -> ~cut l B C.