X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FNpossetoid.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FNpossetoid.ma;h=23363a1709391f140891e0ffed7c39f821598d4b;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma new file mode 100644 index 000000000..23363a170 --- /dev/null +++ b/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma @@ -0,0 +1,70 @@ +(**************************************************************************) +(* ___ *) +(* ||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". + +include "CoRN.ma". + +(* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *) + +include "model/setoids/Nsetoid.ma". + +include "model/structures/Npossec.ma". + +include "algebra/CSetoidFun.ma". + +(*#* **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". +