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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 Pappus line theorem *)
(** This version uses an extra point *)

Theorem Pappus_2 : forall A B C A' B' C' P Q R T:Point,
on_line C A B ->
on_line C' A' B' ->
inter_ll P A' B A B' ->
inter_ll Q A C' A' C ->
inter_ll R B' C B C' ->
inter_ll T B' C P Q ->
C<>R -> C<>T ->
parallel B' R C R ->
parallel B' T C T ->
B'**R / C**R = B'**T / C**T.