(***************************************************************************)
(* 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 area_method.
(* A small lemma to check that centroid is really at the intersection of medians. *)

Lemma centroid_midpoint_centroid_2 : forall A B C G A' B' C' G',
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 ->
Py G G' G = 0.