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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:30"/><i><font color="Green">E19</font></i>: 
 <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:30"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rusub_4.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:30"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="rusub_4.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rusub_4.html#E2:30"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being  <a href="bhsp_1.html#V1">strict</a>  <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:30"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E7:30"/><i><font color="Green">E22</font></i>: 
 <a href="rusub_4.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rusub_4.html#E4:30"><i><font color="Green">E21</font></i></a>, <a class="ref" href="rusub_4.html#D4" target="_self">Def4</a></i>;<br/>
<b>thus </b><a NAME="E8:30"/>
contradiction
 <b>by </b><i><a class="txt" href="rusub_4.html#E1:30"><i><font color="Green">E19</font></i></a>, <a class="txt" href="rusub_4.html#E7:30"><i><font color="Green">E22</font></i></a>, <a class="ref" href="rusub_4.html#T8" target="_self">Th8</a></i>;<br/>


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