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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">V</font> is <a href="rlvect_5.html#V1" target="_self">finite-dimensional</a>
 ;<br/>

<b>consider </b><font color="Maroon">A</font> being    <a href="rlvect_3.html#M1">Basis</a> of <font color="Maroon">W</font>;<br/>
<b>consider </b><font color="Maroon">I</font> being    <a href="rlvect_3.html#M1">Basis</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:30"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:30"/>
<font color="Maroon">I</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:30"/><b>then </b>
<font color="Maroon">A</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="rlvect_5.html#T1" target="_self">Th1</a>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:30"/>
<font color="Maroon">W</font> is <a href="rlvect_5.html#V1" target="_self">finite-dimensional</a>
 <b>by </b><i/>;<br/>


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