(** We choose the most general notion such that l2_11 is still valid *)

Definition  weak_3_parallelogram (A B C D : Point) : Prop :=
  exists O, mid_point O A C /\ mid_point O B D.

Theorem pascalian_ax : forall A B C P Q R : Point, Col A B C -> Col P Q R -> parallel A Q R B -> parallel B P Q C -> parallel A P R C.