(** 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 cop_plane_aux : forall A B C D, Coplanar A B C D -> A <> B -> exists p, IncidentP A p /\ IncidentP B p /\ IncidentP C p /\ IncidentP D p.