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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th8</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: MATROID0:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="matroid0.html#K2" title="MATROID0:func.2">ProdMatroid</a> <font color="Olive" title="b1">P</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">A</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  iff  for <font color="Olive" title="b3">D</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">P</font>  ex <font color="Olive" title="b4">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b3">D</font> st <font color="Olive" title="b2">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Olive" title="b3">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">d</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )</div></div>
