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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_middle :
forall (A B W U V Y : Point) (r : F),
on_parallel_d Y W U V r ->
Py A Y B = Py A W B + r* (Py A V B - Py A U B  + 2* Py W U V  )-r*(1-r)*(Py U V U).