(** 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.

Lemma weak_parallelogram_weak_2_parallelogram : forall A B C D, weak_parallelogram A B C D -> weak_2_parallelogram A B C D.