(** 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_11a_strong_strong_strong_aux : forall A B C D P Q : Point, A=C -> weak_3_parallelogram A B C D -> S A P Q + S C P Q = S B P Q + S D P Q.