(***************************************************************************)
(* 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_left_right : forall Y O U V A ro ru rv,
a_ratio Y O U V ro ru rv ->
Py Y A Y = ro * (ro * Py O A O + ru * Py O A U + rv * Py O A V) +
ru * (ro * Py U A O + ru * Py U A U + rv * Py U A V) +
rv * (ro * Py V A O + ru * Py V A U + rv * Py V A V).