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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: MATROID0:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font> being   non  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  <a href="matroid0.html#NM1" title="MATROID0:NM.1">SubsetFamilyStr</a> holds <br/> ( <font color="Olive" title="b1">M</font> is  <a href="matroid0.html#V1" title="MATROID0:attr.1">subset-closed</a>  iff  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  &amp; <font color="Olive" title="b3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A</font> holds <br/><font color="Olive" title="b3">B</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  )</div></div>
