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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 th6_42 :
forall A B C L M N P K : Point,
is_midpoint M A B ->
is_midpoint N A C ->
is_midpoint K B C ->
is_midpoint L A K ->
on_inter_parallel_parallel P A C M K B N ->
P<>A ->
(2 + 2) * S A K P = (1 + 2) * S A B C.