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[helm.git] / matita / contribs / CoRN-Decl / model / setoids / Npossetoid.ma

diff --git a/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Npossetoid".
+
+include "CoRN.ma".
+
+(* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
+
+include "model/setoids/Nsetoid.ma".
+
+include "model/structures/Npossec.ma".
+
+include "algebra/CSetoidFun.ma".
+
+(*#* **Example of a setoid: [Npos]
+
+*** Setoid
+The positive natural numbers [Npos] will be defined as a subsetoid of the
+natural numbers.
+*)
+
+inline "cic:/CoRN/model/setoids/Npossetoid/Npos.con".
+
+inline "cic:/CoRN/model/setoids/Npossetoid/NposP.con".
+
+(*#* One and two are elements of it.
+*)
+
+inline "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con".
+
+inline "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con".
+
+(*#* ***Addition and multiplication
+Because addition and multiplication preserve positivity, we can define 
+them on this subsetoid.
+*)
+
+inline "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con".
+
+inline "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con".
+
+inline "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con".
+
+inline "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con".
+
+(*#* The addition has no right unit on this set.
+*)
+
+inline "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con".
+
+(*#* And the multiplication doesn't have an inverse, because there can't be an
+inverse for 2.
+*)
+
+inline "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con".
+