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<b>let </b><font color="Maroon" title="c3">n</font>, <font color="Maroon" title="c4">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:31_1_2"/><i><font color="Green" title="E27">A4</font></i>: 
for <font color="Olive" title="b1">I</font> being   <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">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>and </b><br/><a NAME="E2:31_1_2"/><i><font color="Green" title="E28">A5</font></i>: 
for <font color="Olive" title="b1">I</font> being   <a href="vectsp_7.html#M1" title="VECTSP_7:mode.1">Basis</a> of <font color="Maroon" title="c2">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="c4">m</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">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="c2">V</font><b> such that </b><br/><a NAME="E4:31_1_2"/><i><font color="Green" title="E29">A6</font></i>: 
<font color="Maroon" title="c5">A</font> is    <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_9.html#E1:31"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="vectsp_9.html#D1" target="_self" title="VECTSP_9:def.1">Def1</a></i>;<br/>
<a NAME="E5:31_1_2"/>
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m</font> )
 
<b>by </b><i><a class="txt" href="vectsp_9.html#E1:31_1_2"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="vectsp_9.html#E2:31_1_2"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="vectsp_9.html#E4:31_1_2"><i><font color="Green" title="E29">A6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:31_1_2"/>
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m</font>
 ;<br/>


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