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<span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/>

<a NAME="E1:37_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="matroid0.html#K1" title="MATROID0:func.1">the_family_of</a> <font color="Maroon" title="c1">M</font> is  <a href="matroid0.html#NV6" title="MATROID0:NV.6">finite-membered</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matroid0.html#D6" target="_self" title="MATROID0:def.6">Def6</a></span>;<br/>
<a NAME="E2:37_1_1"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matroid0.html#K1" title="MATROID0:func.1">the_family_of</a> <font color="Maroon" title="c1">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matroid0.html#D2" target="_self" title="MATROID0:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:37_1_1"/>
<font color="Maroon" title="c2">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="matroid0.html#D5" target="_self" title="MATROID0:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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