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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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Require Export advanced_parallel_lemmas.
Require Export geometry_tools.
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(*  Elimination Theorems                                               *)
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(* Area elimination *)
unfold on_line in |- *.
Proof with Geometry.
unfold on_inter_parallel_parallel in |- *.
unfold parallel in |- *.
intros.
assert (S4 G C H D = - S4 C G D H)...
rewrite H1 in H0.
intuition.
Qed.

Theorem elim_area_on_line_d :
forall (A B P Q Y : Point) (lambda : F),
on_line_d Y P Q lambda -> S A B Y = lambda * S A B Q + (1 - lambda) * S A B P.