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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="rusub_4.html#V1" target="_self">finite-dimensional</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_3.html#V1">linearly-independent</a> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="rusub_3.html#M1">Basis</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:9"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="rusub_3.html#T15">RUSUB_3:15</a></i>;<br/>
<a NAME="E4:9"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="rusub_4.html#E1:9"><i><font color="Green">E8</font></i></a>, <a class="ref" href="rusub_4.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="txt" href="rusub_4.html#E3:9"><i><font color="Green">E9</font></i></a>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>


</div>
