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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E1:23"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="normsp_1.html#NM2">sequence</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" target="_self">REAL-NS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> is <a href="rsspace3.html#V1">CCauchy</a> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="normsp_1.html#V4">convergent</a>
 
<b>by </b><i><a class="ref" href="real_ns1.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E2:23"/>
 <a href="real_ns1.html#K4" target="_self">REAL-NS</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="lopban_1.html#NM2">RealBanachSpace</a>
 <b>by </b><i><a class="ref" href="lopban_1.html#D16">LOPBAN_1:def 16</a></i>;<br/>


</div>
