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(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
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(* The line going through the midpoints is parallel to the third side *)

Theorem th6_257 :
forall (A B C D P Q R S : Point) (r1 r2 : F),
on_parallel_d D A B C 1 ->
on_line_d S D A r2 ->
on_line_d P A B r1 ->
on_line_d R C D r1 ->
on_line_d Q B C r2 ->
S4 P Q R S = (2 * (r2 * r1) - r2 - r1 + 1) * S4 A B C D.