(** Axiom of Pasch, (Hilbert version). *)

(** First we define a predicate which means that the line l intersects the segment AB. *)

Definition cut := fun l A B =>
  ~ IncidentL A l /\ ~ IncidentL B l /\ exists I, IncidentL I l /\ Between_H A I B.

Lemma plane_cop: forall A B C D p, IncidentP A p -> IncidentP B p -> IncidentP C p -> IncidentP D p -> Coplanar A B C D.