X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FQpossetoid.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fsetoids%2FQpossetoid.ma;h=9557dc175eeb86b1144d4b7fa1b0cdb136844dbb;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=3dc6087f47a80c8ca993702c9ec27650ed95d951;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma b/helm/software/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma index 3dc6087f4..9557dc175 100644 --- a/helm/software/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma +++ b/helm/software/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qpossetoid". +include "CoRN.ma". + (* $Id: Qpossetoid.v,v 1.4 2004/04/06 15:46:05 lcf Exp $ *) -(* INCLUDE -Qsetoid -*) +include "model/setoids/Qsetoid.ma". -(* INCLUDE -CSetoidFun -*) +include "algebra/CSetoidFun.ma". -(* INCLUDE -Qpossec -*) +include "model/structures/Qpossec.ma". (*#* **Example of a setoid: [Qpos] ***Setoid @@ -36,18 +32,18 @@ We will examine the subsetoid of positive rationals of the setoid of rational numbers. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con". -inline cic:/CoRN/model/setoids/Qpossetoid/QposP.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/QposP.con". (*#* One, two and four are elements of it. *) -inline cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con". -inline cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con". -inline cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con". (*#* ***Multiplication As we have seen, multiplication preserves positivity, so we can restrict it @@ -55,49 +51,49 @@ As we have seen, multiplication preserves positivity, so we can restrict it nice properties. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con". -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con". -inline cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con". (*#* ***Inverse We restrict the domain of the inverse to the set of positive rationals. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con". (*#* The restricted inverse preserves positivity. *) -inline cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con". (*#* Now, we can also restrict the co-domain. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con". (*#* This restricted inverse map appears a setoid function. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con". -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con". (*#* ***Special multiplication and inverse We define [multdiv2]: $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con". -inline cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con". -inline cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con". (*#* And its inverse [multdiv4]: $x \mapsto 4/x$ #x ↦ 4/x#. *) -inline cic:/CoRN/model/setoids/Qpossetoid/mult4.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/mult4.con". -inline cic:/CoRN/model/setoids/Qpossetoid/divmult4.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con".