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<b>let </b><font color="Maroon">V</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="rusub_3.html#M1" target="_self">Basis</a> of <font color="Maroon">W</font>;<br/>





<a NAME="E1:31"/>
( <font color="Maroon">A</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">W</font> &amp; <font color="Maroon">A</font> is <a href="rlvect_3.html#V1">linearly-independent</a> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">B</font> = <font color="Maroon">A</font> as  <a href="rlvect_3.html#V1">linearly-independent</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font> <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">I</font> being    <a href="rusub_3.html#M1" target="_self">Basis</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:31"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">I</font>
;<br/>

<b>thus </b><a NAME="E5:31"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/>


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