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

<b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">s'</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c3">s</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> &amp; <font color="Maroon" title="c4">s'</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> )
 ;<br/>

<a NAME="E2:45"/><b>then </b>
<font color="Maroon" title="c3">s</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">s'</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T29" target="_self" title="COMSEQ_2:th.29">Th29</a></i>;<br/>
<b>hence </b> <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">s'</font></span>)</span> <a href="comseq_2.html#K1" title="COMSEQ_2:func.1">*'</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">s'</font></span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="ref" href="comseq_2.html#T12" target="_self" title="COMSEQ_2:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c4">s'</font></span>)</span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> 
<b>by </b><i><a class="txt" href="comseq_2.html#E1:45"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="comseq_2.html#T30" target="_self" title="COMSEQ_2:th.30">Th30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c4">s'</font></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a> </span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T121" title="COMPLEX1:th.121">COMPLEX1:121</a></i>
;<br/><br/>


</div>
