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_plane : forall A B C D, Coplanar A B C D ->
exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.