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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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(* Ratios elimination *)
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(** Test on_line_d in a ratio *)
(* Lemma test_on_line_d_13 : forall Y P Q A C D lambda, on_line_d Y P Q lambda ->  Y<>A -> parallel C D Y A -> False -> C**D/Y**A = C**D. *)
(** Test inter_ll in a ratio *)
(** Test cases where Y occurs both in denominator and numerator *)

Lemma test_on_foot_1 : forall A C D Y R P Q,
on_foot Y R P Q ->
C<>D ->
parallel A Y C D ->
A**Y/C**D = 1-1+ A**Y/C**D.