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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 *)

(* Specifications: *)
Theorem non_zero_denom_on_line_area : forall A B C : Point, on_line A B C -> B <> C.
unfold on_line in |- *.
Theorem non_zero_denom_inter_ll_area :
forall A B C D E : Point, inter_ll A B C D E -> S4 B D C E <> 0.
Theorem non_zero_denom_on_parallel_d_area : forall A B C D : Point, on_parallel A B C D -> C <> D.
Theorem non_zero_denom_on_inter_line_parallel_area :
forall A B C D E G : Point, on_inter_line_parallel A B C D E G -> S4 E C G D <> 0.
Theorem non_zero_denom_on_inter_parallel_parallel_area :
forall A B C D E G H : Point, on_inter_parallel_parallel A B C D E G H -> S4 C G D H <> 0.