(***************************************************************************)
(* 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 pythagoras_difference_lemmas.
Require Export euclidean_constructions_2.
Require Export construction_lemmas_2.
Require Export ratios_elimination_lemmas.

Lemma grid_existence :
forall O U, O<>U ->
exists V,
perp O U O V /\ O**U <> 0 /\ O**V <> 0.