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<b>consider </b><font color="Maroon" title="c2">A</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E2:34_1_1"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c2">A</font> is    <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="rlvect_5.html#E1:34"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="rlvect_5.html#D1" target="_self" title="RLVECT_5:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:34_1_1"/><i><font color="Green" title="E31">A3</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">A</font>
 ;<br/>
<a NAME="E5:34_1_1"/>
for <font color="Olive" title="b1">I</font> being   <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font> holds   <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="txt" href="rlvect_5.html#E1:34"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="rlvect_5.html#E2:34_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="rlvect_5.html#E4:34_1_1"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="rlvect_5.html#T26" target="_self" title="RLVECT_5:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E6:34_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>for <font color="Olive" title="b2">I</font> being   <a href="rlvect_3.html#M1" title="RLVECT_3:mode.1">Basis</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Olive" title="b2">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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