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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_line_d_left_right :
forall (A P Q Y : Point) (f : F),
on_line_d Y P Q f -> Py Y A Y = f* (f * Py Q A Q + (1 - f) * Py Q A P) +
(1 - f) * (f * Py P A Q + (1 - f) * Py P A P) .