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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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><a NAME="E1:47"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rlvect_5.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being  <a href="rlvect_1.html#V2">strict</a>  <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:47"/><i><font color="Green">E37</font></i>: 
 <a href="rlvect_5.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E43"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<b>thus </b><a NAME="E4:47"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="rlvect_5.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E3:47"><i><font color="Green">E37</font></i></a>, <a class="ref" href="rlvect_5.html#D4" target="_self">Def4</a></i>;<br/>


</div>
