<?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="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="rusub_3.html#M1" target="_self">Basis</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:31"/>
( <font color="Maroon">c<sub>3</sub></font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_3.html#V1">linearly-independent</a> )
 
<b>by </b><i><a class="ref" href="rusub_3.html#D2" target="_self">Def2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  <a href="rlvect_3.html#V1">linearly-independent</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="rusub_3.html#T22" target="_self">Th22</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="rusub_3.html#M1" target="_self">Basis</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:31"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="rusub_3.html#T15" target="_self">Th15</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E5:31"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rusub_3.html#E4:31"><i><font color="Green">E21</font></i></a></i>;<br/>


</div>
