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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">g</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<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>assume </b><b>that </b><br/><a NAME="E1:44"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">seq</font> is <a href="clvect_2.html#V1" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E2:44"/><i><font color="Green">E44</font></i>: 
 <a href="clvect_2.html#K1" target="_self">lim</a> <font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E3:44"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">seq</font> <a href="csspace.html#K17">+</a> <font color="Maroon">x</font> is <a href="clvect_2.html#V1" target="_self">convergent</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:44"/>
 <a href="clvect_2.html#K1" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="csspace.html#K17">+</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:44"/>
(  <a href="clvect_2.html#K3" target="_self">dist</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="csspace.html#K17">+</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x</font></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" target="_self">dist</a> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="csspace.html#K17">+</a> <font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, </i>;<br/>


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