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<div><span class="kw">theorem </span><a NAME="T5"><span class="comment"><font color="firebrick">:: CARDFIL2:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1"> { <span class="default"> <font color="Olive" title="b3">B</font> where <font color="Olive" title="b3">B</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> : <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">B</font> </span> } </span>  is    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of <font color="Olive" title="b1">X</font></div></div>
