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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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Require Export pythagoras_difference_lemmas.
Require Export ratios_elimination_lemmas.

Theorem elim_py_on_parallel_d_left_right :
forall (B W U V Y : Point) (r : F),
on_parallel_d Y W U V r ->
Py Y B Y = Py W B W + r * r * Py V B V - 2 * r * r * Py V B U + r * r * Py U B U +
2 * r * Py V B W - 2 * r * Py U B W.