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<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>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="E1:25"/>
<font color="Maroon">A</font> is <a href="vectsp_7.html#V1" target="_self">linearly-independent</a>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E4:25"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">B</font> is <a href="vectsp_7.html#V1" target="_self">linearly-independent</a> &amp;  <a href="vectsp_7.html#K1" target="_self">Lin</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G4">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">V</font> #) )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</font> as    <a href="vectsp_7.html#M1" target="_self">Basis</a> of <font color="Maroon">V</font> <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">B</font>
;<br/>

<b>thus </b><a NAME="E6:25"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/>


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