(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.          *)
(* Julien Narboux (Julien@narboux.fr)                                      *)
(* LIX/INRIA FUTURS 2004-2006                                              *)
(* University of Strasbourg 2008                                           *)
(***************************************************************************)
Require Export area_method.
(* A small lemma to check that centroid is really at the intersection of medians. *)

Lemma centroid_midpoint_centroid : forall A B C G A' B' C' G' X,
is_centroid G A B C ->
is_midpoint A' B C ->
is_midpoint B' A C ->
is_midpoint C' A B ->
is_centroid G' A' B' C' ->
1+2<>0 ->
Col G G' X.