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 out_same_side : forall A B C l, IncidL A l -> ~IncidL B l ->  outH A B C -> same_side B C l.