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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 ConverseMenelauseQuadri :
forall (A B C D A1 B1 C1 D1 : Point) (r1 r2 : F),
mratio B1 B C r1 ->
mratio C1 C D r2 ->
inter_ll D1 D A B1 C1 ->
inter_ll A1 A B B1 C1 ->
A1 <> A ->
D1 <> A ->
parallel B A1 A1 A ->
parallel D D1 D1 A -> B ** A1 / A1 ** A = r1 * (r2 * (D ** D1 / D1 ** A)).