<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: MATROID0:16</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#V1" title="MATROID0:attr.1">subset-closed</a>   <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</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#NM2" title="MATROID0:NM.2">Matroid</a> iff  for <font color="Olive" title="b2">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">M</font><br/>  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <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="Olive" title="b1">M</font>  st <font color="Olive" title="b3">A</font> <a href="matroid0.html#R1" title="MATROID0:pred.1">is_maximal_independent_in</a> <font color="Olive" title="b2">C</font> &amp; <font color="Olive" title="b4">B</font> <a href="matroid0.html#R1" title="MATROID0:pred.1">is_maximal_independent_in</a> <font color="Olive" title="b2">C</font> holds <br/> <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b4">B</font> )</div></div>
