(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008-2009                                      *)
(***************************************************************************)
Require Export euclidean_constructions.
Require Export area_elimination_lemmas.
Require Export ratios_elimination_lemmas.
Require Export Classical.
Ltac cases_per A B C := elim (per_dec A B C);intros.

Lemma l3_5_py : forall A B U V Y,
U <> V ->
Col Y U V ->
Py A Y B = U**Y / U**V * Py A V B + Y**V/ U**V * Py A U B
- (U**Y/ U**V) * (Y**V / U**V) * Py U V U.