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 plane_coplanar : forall A B C D p, IncidP A p -> IncidP B p -> IncidP C p -> IncidP D p ->
Coplanar A B C D.