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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="matrlin.html#V2">finite-dimensional</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:45"/><i><font color="Green">E34</font></i>: 
 <a href="vectsp_9.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>3</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="E2:45"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="vectsp_9.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">c<sub>3</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>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:45"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="vectsp_9.html#K2" target="_self">Subspaces_of</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E2:45"><i><font color="Green">E35</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>5</sub></font> being  <a href="vectsp_1.html#V11">strict</a>  <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E6:45"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E7:45"/><i><font color="Green">E37</font></i>: 
 <a href="vectsp_9.html#K1" target="_self">dim</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E4:45"><i><font color="Green">E36</font></i></a>, <a class="ref" href="vectsp_9.html#D3" target="_self">Def3</a></i>;<br/>
<b>thus </b><a NAME="E8:45"/>
contradiction
 <b>by </b><i><a class="txt" href="vectsp_9.html#E1:45"><i><font color="Green">E34</font></i></a>, <a class="txt" href="vectsp_9.html#E7:45"><i><font color="Green">E37</font></i></a>, <a class="ref" href="vectsp_9.html#T29" target="_self">Th29</a></i>;<br/>


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