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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 area_elimination_lemmas.
Require Export py_elimination_lemmas.
(** Tactics to distinguish cases if necessary *)
(** If S A B C = 0 is in the context then Tac1 is used *)
(** If S A B C <>0 is in the context then Tac2 is used *)
(** othewise we use Col decidability and perform Tac1 and Tac2 in each branch *)
(** We do not use the defiinition Col, to save the burden of managing the unfold *)

Lemma  col_decS : forall A B C:Point, S A B C = 0 \/ S A B C <>0.
Ltac named_cases_colS A B C H := elim (col_decS A B C);intro H.