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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of <font color="Maroon" title="c2">W</font>;<br/>





<a NAME="E1:17"/>
( <font color="Maroon" title="c3">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">W</font> &amp; <font color="Maroon" title="c3">A</font> is <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a> )
 
<b>by </b><i><a class="ref" href="rlvect_3.html#D3" title="RLVECT_3:def.3">RLVECT_3:def 3</a></i>;<br/>
<a NAME="E2:17"/><b>then </b>
<font color="Maroon" title="c3">A</font> is  <a href="rlvect_3.html#V1" title="RLVECT_3:attr.1">linearly-independent</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>
 
<b>by </b><i><a class="ref" href="rlvect_5.html#T15" target="_self" title="RLVECT_5:th.15">Th15</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">I</font> being    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E4:17"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font>
 <b>by </b><i><a class="ref" href="rlvect_5.html#T2" target="_self" title="RLVECT_5:th.2">Th2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">I</font>
;<br/>

<b>thus </b><a NAME="E5:17"/>
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">I</font>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E4:17"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/>


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