(** 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_11b : forall A B C D P Q : Point, parallelogram A B C D -> S4 P A Q B = S4 P D Q C.