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

<a NAME="E1:10"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <a href="csspace.html#K20">Complex_l2_Space</a>  iff ( <font color="Olive">b<sub>1</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> &amp; <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2">seq_id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K11">(#)</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2">seq_id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> is <a href="series_1.html#V1">summable</a> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:10_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="csspace.html#K1">the_set_of_ComplexSequences</a>  iff <font color="Maroon">c<sub>1</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> )
 
<b>by </b><i><a class="ref" href="csspace.html#D1">CSSPACE:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:10_1"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <a href="csspace.html#K20">Complex_l2_Space</a>  iff ( <font color="Maroon">c<sub>1</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> &amp; <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2">seq_id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K11">(#)</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2">seq_id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> is <a href="series_1.html#V1">summable</a> ) )
 <b>by </b><i><a class="ref" href="csspace.html#D11">CSSPACE:def 11</a>, <a class="ref" href="csspace.html#D20">CSSPACE:def 20</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:10"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <a href="csspace.html#K20">Complex_l2_Space</a>  iff ( <font color="Olive">b<sub>1</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> &amp; <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2">seq_id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K11">(#)</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="csspace.html#K2">seq_id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> is <a href="series_1.html#V1">summable</a> ) )
 ;<br/>


</div>
