X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fmonoids%2FZmonoid.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fmonoids%2FZmonoid.ma;h=d6b0ddea47a079c8112f86f5b9dd3907c3cbf5c3;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma new file mode 100644 index 000000000..d6b0ddea4 --- /dev/null +++ b/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma @@ -0,0 +1,57 @@ +(**************************************************************************) +(* ___ *) +(* ||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]. *) +