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

<a NAME="E1:6_1_1"/>
 <a href="csspace.html#K2">seq_id</a> <a href="csspace.html#K6">CZeroseq</a>  is <a href="comseq_2.html#V1">bounded</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">seq</font> =  <a href="csspace.html#K2">seq_id</a> <a href="csspace.html#K6">CZeroseq</a>  as   <a href="comseq_1.html#NM1">Complex_Sequence</a> ;<br/>
<a NAME="E2:6_1_1_1"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   holds <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="comseq_1.html#K1">.</a> <font color="Olive">n</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="xxreal_0.html#R1">&lt;</a> 1
 
<b>by </b><i><a class="ref" href="csspace.html#D6">CSSPACE:def 6</a>, <a class="ref" href="complex1.html#T130">COMPLEX1:130</a></i>;<br/>
<b>hence </b><a NAME="E3:6_1_1_1"/>
 <a href="csspace.html#K2">seq_id</a> <a href="csspace.html#K6">CZeroseq</a>  is <a href="comseq_2.html#V1">bounded</a>
 <b>by </b><i><a class="ref" href="comseq_2.html#T8">COMSEQ_2:8</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:6_1_1"/>
not  <a href="csspace4.html#K1" target="_self">the_set_of_BoundedComplexSequences</a>  is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i/>;<br/>


</div>
