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_construction : forall A B X Y, X <> Y -> A <> B -> exists C, CongH A C X Y /\ (outH A B C).
Definition Para := fun l m =>
(~ exists X, IncidL X l /\ IncidL X m) /\ exists p, IncidLP l p /\ IncidLP m p.