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[helm.git] / matita / contribs / CoRN-Decl / model / monoids / Zmonoid.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/monoids/Zmonoid".
+
+include "CoRN.ma".
+
+(* $Id: Zmonoid.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
+
+include "model/semigroups/Zsemigroup.ma".
+
+include "algebra/CMonoids.ma".
+
+(*#* **Examples of monoids: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
+***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
+We use the addition [ZERO] (defined in the standard library) as the
+unit of monoid:
+*)
+
+inline "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con".
+
+inline "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con".
+
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con".
+
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con".
+
+(*#* The term [Z_as_CMonoid] is of type [CMonoid]. Hence we have proven that [Z] is a constructive monoid.
+
+***$\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
+As the multiplicative unit we should use [`1`], which is [(POS xH)] in
+the representation we have for integers.
+*)
+
+inline "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con".
+
+inline "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con".
+
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con".
+
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con".
+
+(*#* The term [Z_mul_as_CMonoid] is another term of type [CMonoid]. *)
+