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<b>let </b><font color="Maroon">X</font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:112"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">seq</font> is <a href="clvect_2.html#V1" target="_self">convergent</a>
 ;<br/>

<a NAME="E2:112"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">seq</font> <a href="clvect_2.html#K8" target="_self">^\</a> <font color="Maroon">k</font> is    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">seq</font>
 
<b>by </b><i><a class="ref" href="clvect_2.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E3:112"/>
<font color="Maroon">seq</font> <a href="clvect_2.html#K8" target="_self">^\</a> <font color="Maroon">k</font> is <a href="clvect_2.html#V1" target="_self">convergent</a>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E4:112"/>
 <a href="clvect_2.html#K1" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="clvect_2.html#K8" target="_self">^\</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="clvect_2.html#K1" target="_self">lim</a> <font color="Maroon">seq</font>
 <b>by </b><i>, <a class="ref" href="clvect_2.html#T4" target="_self">Th4</a>, </i>;<br/>


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