(** 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 lower_dim' : PA <> PB /\ PB <> PC /\ PA <> PC /\ ~ Col_H PA PB PC.