(** Definition of the collinearity predicate. We say that three points are collinear if they belongs to the same line. *)
Definition Col_H := fun A B C =>
exists l, IncidentL A l /\ IncidentL B l /\ IncidentL C l.
(** We show that the notion of collinearity we just defined is equivalent to the notion of collinearity of Tarski. *)

Lemma cols_coincide : forall A B C, Col A B C <-> Col_H A B C.