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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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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 *)
(* Test in the hypotheses *)
(* Hypotheses and goal tests *)
(* Lemma test14 : forall A B C : Point, S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C=0. *)
(* Lemma test17 : forall A B C D E F G H I J K L : Point, S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C =0 -> 0=0. *)

Lemma test174 : forall A B C P,
S B C P <> 0 ->
S A B P <> 0 ->
S C A P <> 0 ->
False ->
- (S A C P / S B C P * (S B A P / S C A P * (S C B P / S A B P))) = 1.