(***************************************************************************)
(* 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 on_foot_per : forall A B C F,
on_foot F A B C ->
per A F B.