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





<b>assume </b><a NAME="E1:21"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="vectsp_9.html#K1">dim</a> <font color="Maroon">V</font>
 ;<br/>

<b>set </b><font color="Maroon">S</font> =  <a href="pencil_4.html#K5" target="_self">PencilSpace</a> <font color="Maroon">V</font>,<font color="Maroon">k</font>;<br/>
<a NAME="E2:21"/>
not <font color="Maroon">k</font> <a href="vectsp_9.html#K2">Subspaces_of</a> <font color="Maroon">V</font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="ref" href="pencil_4.html#T1" target="_self">Th1</a>, <a class="ref" href="vectsp_9.html#T40">VECTSP_9:40</a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
not  <a href="pencil_4.html#K5" target="_self">PencilSpace</a> <font color="Maroon">V</font>,<font color="Maroon">k</font> is <a href="struct_0.html#V3">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>


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