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<b>consider </b><font color="Maroon">c<sub>3</sub></font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:18_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="matrlin.html#D3" target="_self">Def3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E4:18_1_1"/><i><font color="Green">E13</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:18_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="ref" href="finseq_4.html#T73">FINSEQ_4:73</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM8">FinSequence</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="matrlin.html#E4:18_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>thus </b><a NAME="E7:18_1_1"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="txt" href="matrlin.html#E5:18_1_1"><i><font color="Green">E14</font></i></a></i>;<br/>

<b>thus </b><a NAME="E8:18_1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> is    <a href="vectsp_7.html#M1">Basis</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="matrlin.html#E2:18_1_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="matrlin.html#E4:18_1_1"><i><font color="Green">E13</font></i></a></i>;<br/>


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