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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_3.html#V1">linearly-independent</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:2"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:2"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_3.html#V1">linearly-independent</a> &amp;  <a href="rlvect_3.html#K1">Lin</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#G2">RLSStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">c<sub>1</sub></font> #) )
 <b>by </b><i><a class="ref" href="rlvect_3.html#T27">RLVECT_3:27</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="rlvect_3.html#M1">Basis</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="rlvect_5.html#E4:2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="rlvect_3.html#D3">RLVECT_3:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E6:2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E3:2"><i><font color="Green">E3</font></i></a></i>;<br/>


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