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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th4</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: MATROID0:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   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#V2" title="MATROID0:attr.2">with_exchange_property</a>  iff  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</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="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> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/> ex <font color="Olive" title="b4">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">M</font> st <br/>( <font color="Olive" title="b4">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">B</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  ) )</div></div>
