X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FZsetoid.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FZsetoid.ma;h=84541c4db7cf2c478c1eea3a334f5e889f21a162;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma new file mode 100644 index 000000000..84541c4db --- /dev/null +++ b/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma @@ -0,0 +1,84 @@ +(**************************************************************************) +(* ___ *) +(* ||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/Zsetoid". + +include "CoRN.ma". + +(* $Id: Zsetoid.v,v 1.5 2004/04/07 15:08:08 lcf Exp $ *) + +include "model/structures/Zsec.ma". + +include "algebra/CSetoidFun.ma". + +(*#* **Example of a setoid: [Z] +*** [Z] +*) + +inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con". + +(*#* The term [Z_as_CSetoid] is of type [CSetoid]. Hence we have proven that [Z] is a constructive setoid. +***Addition +We will prove now that the addition on the integers is a setoid function. +*) + +inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con". + +(*#* What's more: the addition is also associative and commutative. +*) + +inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con". + +(*#* ***Opposite +Taking the opposite of an integer is a setoid function. +*) + +inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con". + +(*#* ***Multiplication +Finally the multiplication is a setoid function and is associative and commutative. +*) + +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con". + +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con". +