(***************************************************************************)
(* Formalization of the Chou, Gao and Zhang's decision procedure.*)
(* Julien Narboux (Julien.Narboux@inria.fr)                                     *)
(* LIX/INRIA FUTURS 2004-2008                                                     *)
(***************************************************************************)
Set Nested Proofs Allowed.
Require Export area_elimination_lemmas.
(** For the first time, we need decidability of the parallel predicate *)

Lemma parallel_dec : forall A B C D, parallel A B C D \/ ~ parallel A B C D.
Ltac cases_parallel A B C D := elim (parallel_dec A B C D);intros.