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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="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:24"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="matrlin.html#V2">finite-dimensional</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E2:24"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="vectsp_7.html#V1">linearly-independent</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:24"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="vectsp_9.html#E1:24"><i><font color="Green">E23</font></i></a>, <a class="ref" href="vectsp_9.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E6:24"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="txt" href="vectsp_9.html#E4:24"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>


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