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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.

Lemma elim_py_midpoint_left_right : forall A B C M : Point,
on_line_d M B C (1 / 2) ->
Py M A M = - (1)/(2+2) * (Py B C B - 2* Py A C A - 2 *Py A B A).