(** 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.

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