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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c1">V</font> is <a href="rusub_4.html#V1" title="RUSUB_4:attr.1">finite-dimensional</a> &amp; <font color="Maroon" title="c2">A</font> is <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">B</font> being    <a href="rusub_3.html#M1" title="RUSUB_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E3:9"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="ref" href="rusub_3.html#T15" title="RUSUB_3:th.15">RUSUB_3:15</a></i>;<br/>
<a NAME="E4:9"/>
<font color="Maroon" title="c3">B</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="rusub_4.html#E1:9"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="rusub_4.html#T3" target="_self" title="RUSUB_4:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon" title="c2">A</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="rusub_4.html#E3:9"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>


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