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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 2008-2009                                       *)
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Require Export area_coords_constructions.
(* Those lemma are not proved as they are used only in a optimisation of the method. *)

Lemma elim_py_a_ratio_middle : forall Y O U V A B ro ru rv,
a_ratio Y O U V ro ru rv ->
Py A Y B = ro * Py A O B + ru * Py A U B + rv * Py A V B
- ro*ru*Py O U O - ro*ru*Py O V O - ru*rv * Py U V U.