(** 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.
(** We show that this definition is equivalent to the predicate TS of Tarski. *)

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.