(***************************************************************************)
(* 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_9 : forall P Q R S A B C D,
parallel P R A C ->
parallel Q S B D ->
B<>D -> A<>C -> ~ perp A C B D ->
Py4 P Q R S / Py4 A B C D = (P**R / A**C) * (Q**S / B**D).