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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="comseq_2.html#V2">convergent</a>
 ;<br/>

<a NAME="E2:44"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">c<sub>1</sub></font> is    <a href="comseq_3.html#M1">subsequence</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="cfcont_1.html#T38" target="_self">Th38</a></i>;<br/>
<b>hence </b><a NAME="E3:44"/>
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">c<sub>1</sub></font> is <a href="comseq_2.html#V2">convergent</a>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E1:44"><i><font color="Green">E31</font></i></a>, <a class="ref" href="cfcont_1.html#T39" target="_self">Th39</a></i>;<br/>

<b>thus </b><a NAME="E4:44"/>
 <a href="comseq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_3.html#K6">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E1:44"><i><font color="Green">E31</font></i></a>, <a class="txt" href="cfcont_1.html#E2:44"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cfcont_1.html#T40" target="_self">Th40</a></i>;<br/>


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