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(* 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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(* The line going through the midpoints is parallel to the third side *)

Theorem gauss_line :
forall A0 A1 A2 A3 X Y M1 M2 M3 : Point,
inter_ll X A0 A3 A1 A2 ->
inter_ll Y A2 A3 A1 A0 ->
is_midpoint M1 A1 A3 ->
is_midpoint M2 A0 A2 ->
is_midpoint M3 X Y ->
S A0 A1 A2 <> 0 ->
Col M1 M2 M3.