<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#NM1">MetrSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tbsp_1.html#V2">convergent</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:20"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="metric_6.html#R1" target="_self">is_convergent_in_metrspace_to</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="metric_6.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E4:20"/>
 <a href="tbsp_1.html#K1">lim</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="metric_6.html#E3:20"><i><font color="Green">E17</font></i></a>, <a class="ref" href="metric_6.html#T26" target="_self">Th26</a></i>;<br/>
<b>hence </b><a NAME="E5:20"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="metric_6.html#R1" target="_self">is_convergent_in_metrspace_to</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="tbsp_1.html#K1">lim</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="metric_6.html#E3:20"><i><font color="Green">E17</font></i></a></i>;<br/>


</div>
