X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FZsetoid.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FZsetoid.ma;h=84541c4db7cf2c478c1eea3a334f5e889f21a162;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=36b8ce6c9dc40a750dda0ff3ae14a3e242f66e77;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma b/helm/software/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma index 36b8ce6c9..84541c4db 100644 --- a/helm/software/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma +++ b/helm/software/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma @@ -16,71 +16,69 @@ 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 -Zsec -*) +include "model/structures/Zsec.ma". -(* INCLUDE -CSetoidFun -*) +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_irreflexive.con". -inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.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_cotransitive.con". -inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.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/ap_Z_is_apartness.con". -inline cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.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_wd.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con. +inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.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_assoc.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.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_wd.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con. +inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.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_wd.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.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_bin_fun.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con. +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con". -inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con. +inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con".