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<b>let </b><font color="Maroon">V</font> be  <a href="rusub_4.html#V1" target="_self">finite-dimensional</a> <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:29"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">V</font>
 ;<br/>

<b>then consider </b><font color="Maroon">W</font> being  <a href="bhsp_1.html#V1">strict</a>  <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:29"/><i><font color="Green">E26</font></i>: 
 <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:29"/>
not <font color="Maroon">n</font> <a href="rusub_4.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">V</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, </i>;<br/>


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