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<b>let </b><font color="Maroon" title="c1">GF</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c3">V</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">VectSp</a> of <font color="Maroon" title="c1">GF</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:45"/><i><font color="Green" title="E34">A1</font></i>: 
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c3">V</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font>
 <b>and </b><br/><a NAME="E2:45"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c3">V</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:45"/><i><font color="Green" title="E36">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">n</font> <a href="vectsp_9.html#K2" title="VECTSP_9:func.2">Subspaces_of</a> <font color="Maroon" title="c3">V</font>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E2:45"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">W</font> being  <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V</font><b> such that </b><br/><a NAME="E6:45"/>
<font color="Maroon" title="c5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font>
 <b>and </b><br/><a NAME="E7:45"/><i><font color="Green" title="E37">A4</font></i>: 
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E4:45"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="vectsp_9.html#D3" target="_self" title="VECTSP_9:def.3">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" title="E34">A1</font></i></a>, <a class="txt" href="vectsp_9.html#E7:45"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="vectsp_9.html#T29" target="_self" title="VECTSP_9:th.29">Th29</a></i>;<br/>


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