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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 MenelausQuadri :
forall A B C D X Y A1 B1 C1 D1 : Point,
inter_ll A1 A B X Y ->
inter_ll B1 B C X Y ->
inter_ll C1 C D X Y ->
inter_ll D1 A D X Y ->
B <> A1 ->
C <> B1 ->
D <> C1 ->
A <> D1 ->
parallel A A1 B A1 ->
parallel B B1 C B1 ->
parallel C C1 D C1 ->
parallel D D1 A D1 ->
A ** A1 / B ** A1 * (B ** B1 / C ** B1 * (C ** C1 / D ** C1 * (D ** D1 / A ** D1))) =
1.