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