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-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(*i $Id: Transitive_Closure.v,v 1.1.2.1 2004/07/16 19:31:42 herbelin Exp $ i*)
-
-(** Author: Bruno Barras *)
-
-Require Relation_Definitions.
-Require Relation_Operators.
-
-Section Wf_Transitive_Closure.
-  Variable A: Set.
-  Variable R: (relation A).
-
-  Notation trans_clos := (clos_trans A R).
- 
-  Lemma incl_clos_trans: (inclusion A R trans_clos).
-    Red;Auto with sets.
-  Qed.
-
-  Lemma Acc_clos_trans: (x:A)(Acc A R x)->(Acc A trans_clos x).
-    NewInduction 1 as [x0 _ H1].
-    Apply Acc_intro.
-    Intros y H2.
-    NewInduction H2;Auto with sets.
-    Apply Acc_inv with y ;Auto with sets.
-  Qed.
-
-  Hints Resolve Acc_clos_trans.
-
-  Lemma Acc_inv_trans: (x,y:A)(trans_clos y x)->(Acc A R x)->(Acc A R y).
-  Proof.
-    NewInduction 1 as [|x y];Auto with sets.
-    Intro; Apply Acc_inv with y; Assumption.
-  Qed.
-
-  Theorem wf_clos_trans: (well_founded A R)  ->(well_founded A trans_clos).
-  Proof.
-    Unfold well_founded;Auto with sets.
-  Qed.
-
-End Wf_Transitive_Closure.