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<b>let </b><font color="Maroon">seq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:48"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">seq</font> is <a href="comseq_2.html#V2">convergent</a>
 <b>and </b><br/><a NAME="E2:48"/><i><font color="Green">E55</font></i>: 
 <a href="comseq_2.html#K2">lim</a> <font color="Maroon">seq</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:48"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">seq</font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">k</font> is <a href="comseq_1.html#V1">non-zero</a>
 <b>by </b><i>, , </i>;<br/>
<b>take </b>
<font color="Maroon">seq</font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">k</font>
;<br/>

<b>thus </b><a NAME="E5:48"/>
( <font color="Maroon">seq</font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">k</font> is    <a href="comseq_3.html#M1">subsequence</a> of <font color="Maroon">seq</font> &amp; <font color="Maroon">seq</font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">k</font> is <a href="comseq_1.html#V1">non-zero</a> )
 <b>by </b><i>, </i>;<br/>


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