--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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".
+
+(* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
+
+(* INCLUDE
+Nsetoid
+*)
+
+(* INCLUDE
+Npossec
+*)
+
+(* INCLUDE
+CSetoidFun
+*)
+
+(*#* **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.
+