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

include "CoRN.ma".

(* $Id: Npossemigroup.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)

include "algebra/CSemiGroups.ma".

include "model/semigroups/Nsemigroup.ma".

include "model/setoids/Npossetoid.ma".

(*#* **Examples of semi-groups:  $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
The positive natural numbers form together with addition a subsemigroup 
 of the semigroup of the natural numbers with addition.
*)

inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con" as definition.

(*#* ***$\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
Also together with multiplication, the positive numbers form a semigroup.
*)

inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con" as lemma.

inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con" as definition.