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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 field_general_properties.
Require Export chou_gao_zhang_axioms.
(* This file contains the lemmas needed by the tactics used as tools for both the development and the decision procedure. *)
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(* Signed areas                                         *)
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auto with Geom.
Qed.
auto with Geom.
Qed.
Hint Resolve S_1: Geom.
Proof with try solve [ Geometry | congruence ].
intros...
assert (S A B C = - S B A C)...
assert (S B A C = S C B A)...
Qed.
Hint Resolve S_2: Geom.
Proof with try solve [ Geometry | congruence ].
intros...
assert (S A B C = - S B A C)...
assert (S B A C = S A C B)...
Qed.
Hint Resolve S_3: Geom.

Lemma S_4 : forall A B C : Point, S A B C = - S B A C.