(***************************************************************************)
(* 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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Ltac local_uniformize_signed_areas := Runiformize_signed_areas.
(* Ltac local_uniformize_signed_areas := uniformize_signed_areas. *)
Ltac local_basic_simpl := Rbasic_simpl.
Ltac local_uniformize_signed_areas4 := uniformize_signed_areas4.
(* Tests uniformize in the goal *)

(* Specifications: *)
Lemma test1 : forall A B C :Point, S A B C = S B C A.
Lemma test2 : forall A B C :Point, S A B C + S B A C = 0.
Lemma test3 : forall A B C :Point, S A B C + S A C B = 0.
Lemma test4 : forall A B C :Point, S A B C +- S B C A = 0.
Lemma test5 : forall A B C :Point, S A B C - S C A B = 0.
Lemma test6 : forall A B C :Point, S A B C + S C B A = 0.
(* Test in the hypotheses *)
Lemma test7 : forall A B C :Point, S A B C + S B A C = 0 -> 0=0.
Lemma test8 : forall A B C :Point, S A B C + S A C B = 0 -> 0=0.
Lemma test9 : forall A B C :Point, S A B C - S B C A = 0 -> 0=0.
Lemma test10 : forall A B C :Point, S A B C - S C A B = 0 -> 0=0.
Lemma test11 : forall A B C :Point, S A B C + S C B A = 0 -> 0=0.
(* Hypotheses and goal tests *)
Lemma test12 : forall A B C :Point, S A B C - S C A B = 0 -> S A B C + S C B A = 0.
Lemma test13 : forall A B C :Point, S A B C + S C B A = 0 ->
S A B C + S B A C = 0 -> S A B C - S B C A = 0 .