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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">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>assume </b><a NAME="E1:112"/><i><font color="Green" title="E57">A1</font></i>: 
<font color="Maroon" title="c2">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 ;<br/>

<a NAME="E2:112"/><i><font color="Green" title="E58">A2</font></i>: 
<font color="Maroon" title="c2">seq</font> <a href="clvect_2.html#K8" title="CLVECT_2:func.8">^\</a> <font color="Maroon" title="c3">k</font> is    <a href="bhsp_3.html#M1" title="BHSP_3:mode.1">subsequence</a> of <font color="Maroon" title="c2">seq</font>
 
<b>by </b><i><a class="ref" href="clvect_2.html#T99" target="_self" title="CLVECT_2:th.99">Th99</a></i>;<br/>
<b>hence </b><a NAME="E3:112"/>
<font color="Maroon" title="c2">seq</font> <a href="clvect_2.html#K8" title="CLVECT_2:func.8">^\</a> <font color="Maroon" title="c3">k</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 <b>by </b><i><a class="txt" href="clvect_2.html#E1:112"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="clvect_2.html#T88" target="_self" title="CLVECT_2:th.88">Th88</a></i>;<br/>

<b>thus </b><a NAME="E4:112"/>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="clvect_2.html#K8" title="CLVECT_2:func.8">^\</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font>
 <b>by </b><i><a class="txt" href="clvect_2.html#E1:112"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="clvect_2.html#E2:112"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="clvect_2.html#T89" target="_self" title="CLVECT_2:th.89">Th89</a></i>;<br/>


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