(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
(***************************************************************************)
Require Export construction_lemmas.
Definition weak_parallelogram (A B C D : Point) : Prop :=
A<>C /\ B<>D /\
exists O, mid_point O A C /\ mid_point O B D.

(* Specifications: *)
Lemma parallelogram_weak_parallelogram : forall A B C D,
parallelogram A B C D -> weak_parallelogram A B C D.
Theorem weak_parallelogram_parallelogram : forall A B C D,
~ Col A B C -> weak_parallelogram A B C D -> parallelogram A B C D.