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<b>let </b><font color="Maroon" title="c1">GF</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">VectSp</a> of <font color="Maroon" title="c1">GF</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>;<br/>





<b>assume </b><a NAME="E1:26"/>
 <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E3:26"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font>
 <b>and </b><br/><a NAME="E4:26"/><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c4">B</font> is <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a> &amp;  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> )
 <b>by </b><i><a class="ref" href="vectsp_7.html#T23" target="_self" title="VECTSP_7:th.23">Th23</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">B</font> = <font color="Maroon" title="c4">B</font> as    <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="vectsp_7.html#E4:26"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="vectsp_7.html#D3" target="_self" title="VECTSP_7:def.3">Def3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">B</font>
;<br/>

<b>thus </b><a NAME="E6:26"/>
<font color="Maroon" title="c5">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="vectsp_7.html#E3:26"><i><font color="Green" title="E14">A1</font></i></a></i>;<br/>


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