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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E2:51"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E3:51"/><i><font color="Green">E31</font></i>: 
 <a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="complex1.html#K5">0c</a> 
 <b>and </b><br/><a NAME="E4:51"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="comseq_1.html#V1">non-zero</a>
 ;<br/>

<a NAME="E5:51"/>
<font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K7">"</a>  is <a href="comseq_2.html#V2" target="_self">convergent</a>
 
<b>by </b><i><a class="txt" href="comseq_2.html#E2:51"><i><font color="Green">E30</font></i></a>, <a class="txt" href="comseq_2.html#E3:51"><i><font color="Green">E31</font></i></a>, <a class="txt" href="comseq_2.html#E4:51"><i><font color="Green">E32</font></i></a>, <a class="ref" href="comseq_2.html#T34" target="_self">Th34</a></i>;<br/>
<b>then </b> <a href="comseq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K3">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K7">"</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K7">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="comseq_2.html#E1:51"><i><font color="Green">E29</font></i></a>, <a class="ref" href="comseq_2.html#T30" target="_self">Th30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="comseq_2.html#E2:51"><i><font color="Green">E30</font></i></a>, <a class="txt" href="comseq_2.html#E3:51"><i><font color="Green">E31</font></i></a>, <a class="txt" href="comseq_2.html#E4:51"><i><font color="Green">E32</font></i></a>, <a class="ref" href="comseq_2.html#T35" target="_self">Th35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K13">/</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
;<br/>
<b>hence </b><a NAME="E7:51"/>
 <a href="comseq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K8">/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K13">/</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="comseq_1.html#D12">COMSEQ_1:def 12</a></i>;<br/>


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