X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fftc%2FFunctSums.ma;h=aeed9200cd628be08d26e015b0ff7aac0b3226cd;hb=80110e17ef1d38d71473e9471ce15beddde663bb;hp=5006a55f98b7ba36b8222f3768ea11b864043c31;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSums.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSums.ma index 5006a55f9..aeed9200c 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSums.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSums.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSums". +include "CoRN.ma". + (* $Id: FunctSums.v,v 1.5 2004/04/23 10:00:59 lcf Exp $ *) (*#* printing FSum0 %\ensuremath{\sum_0}% #∑0# *) @@ -24,13 +26,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSums". (*#* printing FSumx %\ensuremath{\sum'}% #∑'&*) -(* INCLUDE -CSumsReals -*) +include "reals/CSumsReals.ma". -(* INCLUDE -PartFunEquality -*) +include "ftc/PartFunEquality.ma". (*#* *Sums of Functions @@ -48,9 +46,9 @@ $\sum_{i=m}^nf_i$#the sum of fm through fn# ( [FSum]). *) -inline cic:/CoRN/ftc/FunctSums/FSum0.con. +inline "cic:/CoRN/ftc/FunctSums/FSum0.con". -inline cic:/CoRN/ftc/FunctSums/FSum.con. +inline "cic:/CoRN/ftc/FunctSums/FSum.con". (*#* Although [FSum] is here defined directly, it has the same relationship @@ -62,37 +60,37 @@ mentioned, their forming too big a type makes it impossible to use those results. *) -inline cic:/CoRN/ftc/FunctSums/FSum_FSum0.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_FSum0.con". -inline cic:/CoRN/ftc/FunctSums/FSum0_wd.con. +inline "cic:/CoRN/ftc/FunctSums/FSum0_wd.con". -inline cic:/CoRN/ftc/FunctSums/FSum_one.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_one.con". -inline cic:/CoRN/ftc/FunctSums/FSum_FSum.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_FSum.con". -inline cic:/CoRN/ftc/FunctSums/FSum_first.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_first.con". -inline cic:/CoRN/ftc/FunctSums/FSum_last.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_last.con". -inline cic:/CoRN/ftc/FunctSums/FSum_last'.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_last'.con". -inline cic:/CoRN/ftc/FunctSums/FSum_wd.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_wd.con". -inline cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con". -inline cic:/CoRN/ftc/FunctSums/inv_FSum.con. +inline "cic:/CoRN/ftc/FunctSums/inv_FSum.con". -inline cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con". -inline cic:/CoRN/ftc/FunctSums/FSum_wd'.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_wd'.con". -inline cic:/CoRN/ftc/FunctSums/FSum_resp_less.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_resp_less.con". -inline cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con". -inline cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con". -inline cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con". (*#* Also important is the case when we have a finite family @@ -100,15 +98,15 @@ $\{f_i\}_{i=0}^{n-1}$ of #exactly n# functions; in this case we need to use the [FSumx] operator. *) -inline cic:/CoRN/ftc/FunctSums/FSumx.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx.con". (*#* This operator is well defined, as expected. *) -inline cic:/CoRN/ftc/FunctSums/FSumx_wd.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_wd.con". -inline cic:/CoRN/ftc/FunctSums/FSumx_wd'.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_wd'.con". (*#* As was already the case for [Sumx], in many cases we will need to @@ -117,9 +115,9 @@ explicitly assume that $f_i$#f1# is independent of the proof that function $f_i$#fi#. *) -inline cic:/CoRN/ftc/FunctSums/ext_fun_seq.con. +inline "cic:/CoRN/ftc/FunctSums/ext_fun_seq.con". -inline cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con. +inline "cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con". (* UNEXPORTED Implicit Arguments ext_fun_seq [n]. @@ -133,35 +131,35 @@ Implicit Arguments ext_fun_seq' [n]. Under these assumptions, we can characterize the domain and the value of the sum function from the domains and values of the summands: *) -inline cic:/CoRN/ftc/FunctSums/FSumx_pred.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_pred.con". -inline cic:/CoRN/ftc/FunctSums/FSumx_pred'.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_pred'.con". -inline cic:/CoRN/ftc/FunctSums/FSumx_char.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_char.con". (*#* As we did for arbitrary groups, it is often useful to rewrite this sums as ordinary sums. *) -inline cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con". -inline cic:/CoRN/ftc/FunctSums/FSumx_lt.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_lt.con". -inline cic:/CoRN/ftc/FunctSums/FSumx_le.con. +inline "cic:/CoRN/ftc/FunctSums/FSumx_le.con". -inline cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con". (*#* Some useful lemmas follow. *) -inline cic:/CoRN/ftc/FunctSums/FSum0_0.con. +inline "cic:/CoRN/ftc/FunctSums/FSum0_0.con". -inline cic:/CoRN/ftc/FunctSums/FSum0_S.con. +inline "cic:/CoRN/ftc/FunctSums/FSum0_S.con". -inline cic:/CoRN/ftc/FunctSums/FSum_0.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_0.con". -inline cic:/CoRN/ftc/FunctSums/FSum_S.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_S.con". -inline cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con. +inline "cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con".