(** 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 Incid_line :
forall P A B l, A<>B ->
IncidentL A l -> IncidentL B l -> Col P A B -> IncidentL P l.