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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="E1:51"/><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="E2:51"/><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>let </b><font color="Maroon">seq1</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:51"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">seq1</font> is    <a href="comseq_3.html#M1">subsequence</a> of <font color="Maroon">seq</font>
 <b>and </b><br/><a NAME="E4:51"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">seq1</font> is <a href="comseq_1.html#V1">non-zero</a>
 ;<br/>

<a NAME="E5:51"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">seq1</font> is <a href="comseq_2.html#V2">convergent</a>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:51"/>
 <a href="comseq_2.html#K2">lim</a> <font color="Maroon">seq1</font> <a href="hidden.html#R1">=</a>  <a href="comseq_2.html#K2">lim</a> <font color="Maroon">seq</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E7:51"/>
 <a href="comseq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">seq1</font> <a href="comseq_1.html#K7">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">seq</font></span>)</span> <a href="complex1.html#K12">"</a> 
 <b>by </b><i>, , , <a class="ref" href="comseq_2.html#T35">COMSEQ_2:35</a></i>;<br/>


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