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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c2">seq</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 ;<br/>

<a NAME="E2:44"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">k</font> is    <a href="comseq_3.html#M1" title="COMSEQ_3:mode.1">subsequence</a> of <font color="Maroon" title="c2">seq</font>
 
<b>by </b><i><a class="ref" href="cfcont_1.html#T38" target="_self" title="CFCONT_1:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E3:44"/>
<font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">k</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E1:44"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T39" target="_self" title="CFCONT_1:th.39">Th39</a></i>;<br/>

<b>thus </b><a NAME="E4:44"/>
 <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq</font>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E1:44"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="cfcont_1.html#E2:44"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="cfcont_1.html#T40" target="_self" title="CFCONT_1:th.40">Th40</a></i>;<br/>


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