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

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">V</font> be  <a href="rlvect_5.html#V1" target="_self">finite-dimensional</a> <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:48"/><i><font color="Green">E31</font></i>: 
 <a href="rlvect_5.html#K1" target="_self">dim</a> <font color="Maroon">V</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:48"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">n</font> <a href="rlvect_5.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">V</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">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:48"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font> <a href="rlvect_5.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">W</font> being  <a href="rlvect_1.html#V2">strict</a>  <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E6:48"/>
<font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E7:48"/><i><font color="Green">E34</font></i>: 
 <a href="rlvect_5.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><a class="ref" href="rlvect_5.html#T2" target="_self">Th2</a>, </i>;<br/>
<b>thus </b><a NAME="E8:48"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="rlvect_5.html#T1" target="_self">Th1</a></i>;<br/>


</div>
