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

<b>let </b><font color="Maroon">GF</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">GF</font>;<br/>



<b>assume </b><a NAME="E1:24"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">V</font> is <a href="matrlin.html#V2">finite-dimensional</a>
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E2:24"/>
<font color="Maroon">A</font> is <a href="vectsp_7.html#V1">linearly-independent</a>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being    <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E4:24"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="vectsp_7.html#T27">VECTSP_7:27</a></i>;<br/>
<a NAME="E5:24"/>
<font color="Maroon">B</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:24"/>
<font color="Maroon">A</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>


</div>
