(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
(**************************************************************************)

(* This file was automatically generated: do not edit *********************)

include "Coq.ma".

(*#***********************************************************************)

(*  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: Newman.v,v 1.7.2.1 2004/07/16 19:31:16 herbelin Exp $ i*)

include "Relations/Rstar.ma".

(* UNEXPORTED
Section Newman
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/A.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/R.var
*)

(* UNAVAILABLE OBJECT: cic:/Coq/Relations/Newman/Newman/Rstar.con *********)

inline procedural "cic:/Coq/Relations/Newman/Newman/Rstar.con" "Newman__" as definition.

(* UNAVAILABLE OBJECT: cic:/Coq/Relations/Newman/Newman/Rstar_reflexive.con *)

inline procedural "cic:/Coq/Relations/Newman/Newman/Rstar_reflexive.con" "Newman__" as definition.

(* UNAVAILABLE OBJECT: cic:/Coq/Relations/Newman/Newman/Rstar_transitive.con *)

inline procedural "cic:/Coq/Relations/Newman/Newman/Rstar_transitive.con" "Newman__" as definition.

(* UNAVAILABLE OBJECT: cic:/Coq/Relations/Newman/Newman/Rstar_Rstar'.con **)

inline procedural "cic:/Coq/Relations/Newman/Newman/Rstar_Rstar'.con" "Newman__" as definition.

inline procedural "cic:/Coq/Relations/Newman/coherence.con" as definition.

inline procedural "cic:/Coq/Relations/Newman/coherence_intro.con" as theorem.

(*#* A very simple case of coherence : *)

inline procedural "cic:/Coq/Relations/Newman/Rstar_coherence.con" as lemma.

(*#* coherence is symmetric *)

inline procedural "cic:/Coq/Relations/Newman/coherence_sym.con" as lemma.

inline procedural "cic:/Coq/Relations/Newman/confluence.con" as definition.

inline procedural "cic:/Coq/Relations/Newman/local_confluence.con" as definition.

inline procedural "cic:/Coq/Relations/Newman/noetherian.con" as definition.

(* UNEXPORTED
Section Newman_section
*)

(*#* The general hypotheses of the theorem *)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Hyp1.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Hyp2.var
*)

(*#* The induction hypothesis *)

(* UNEXPORTED
Section Induct
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/x.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/hyp_ind.var
*)

(*#* Confluence in [x] *)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/y.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/z.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/h1.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/h2.var
*)

(*#* particular case [x->u] and [u->*y]   *)

(* UNEXPORTED
Section Newman_
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/Newman_/u.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/Newman_/t1.var
*)

(* UNEXPORTED
cic:/Coq/Relations/Newman/Newman/Newman_section/Induct/Newman_/t2.var
*)

(*#* In the usual diagram, we assume also [x->v] and [v->*z] *)

inline procedural "cic:/Coq/Relations/Newman/Diagram.con" as theorem.

inline procedural "cic:/Coq/Relations/Newman/caseRxy.con" as theorem.

(*i case x->v->*z i*)

(* UNEXPORTED
End Newman_
*)

inline procedural "cic:/Coq/Relations/Newman/Ind_proof.con" as theorem.

(*i case x->u->*z i*)

(* UNEXPORTED
End Induct
*)

inline procedural "cic:/Coq/Relations/Newman/Newman.con" as theorem.

(* UNEXPORTED
End Newman_section
*)

(* UNEXPORTED
End Newman
*)