Definition cut' A B X Y := X <> Y /\ forall l, IncidL X l -> IncidL Y l -> cut l A B.
Global Instance cut_morphism : Proper(EqL ==> eq ==> eq ==> iff) cut.

Lemma coplanar_plane1 : forall A B C D X,
(Bet A B X \/ Bet B X A \/ Bet X A B) -> (Bet C D X \/ Bet D X C \/ Bet X C D) ->
exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.