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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: Qmonoid.v,v 1.7 2004/04/08 08:20:33 lcf Exp $ *)

include "model/semigroups/Qsemigroup.ma".

include "algebra/CMonoids.ma".

(*#* **Examples of a monoid: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
The rational numbers form with addition a CMonoid. [QZERO] is the unit.
*)

inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con" as lemma.

inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con" as lemma.

inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con" as definition.

inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con" as definition.

(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
Also with multiplication Q forms a CMonoid. Here, the unit is [QONE].
*)

inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con" as lemma.

inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con" as lemma.

inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con" as definition.

inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con" as definition.