<?xml version="1.0"?>
<div class="add">

<a NAME="E1:3_1_1"/>
 <a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <a href="csspace.html#K6" title="CSSPACE:func.6">CZeroseq</a>  is <a href="comseq_3.html#V2" title="COMSEQ_3:attr.2">absolutely_summable</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c1">cseq</font> =  <a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <a href="csspace.html#K6" title="CSSPACE:func.6">CZeroseq</a>  as   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a> ;<br/>
<a NAME="E2:3_1_1_1"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">cseq</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 
<b>by </b><i><a class="ref" href="csspace.html#D6" title="CSSPACE:def.6">CSSPACE:def 6</a></i>;<br/>
<b>hence </b><a NAME="E3:3_1_1_1"/>
 <a href="csspace.html#K2" title="CSSPACE:func.2">seq_id</a> <a href="csspace.html#K6" title="CSSPACE:func.6">CZeroseq</a>  is <a href="comseq_3.html#V2" title="COMSEQ_3:attr.2">absolutely_summable</a>
 <b>by </b><i><a class="ref" href="comseq_3.html#T52" title="COMSEQ_3:th.52">COMSEQ_3:52</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:3_1_1"/>
not  <a href="csspace3.html#K1" title="CSSPACE3:func.1">the_set_of_l1ComplexSequences</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="csspace3.html#D1" target="_self" title="CSSPACE3:def.1">Def1</a></i>;<br/>


</div>
