(** 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 l2_12b : forall A B C D P : Point, parallelogram A B C D -> S P A B = S4 P D A C.