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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: CARDFIL2:57</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">F1</font>, <font color="Olive" title="b3">F2</font>, <font color="Olive" title="b4">F</font> being    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b4">F</font> <a href="cardfil2.html#R2" title="CARDFIL2:pred.2">is_filter-finer_than</a> <font color="Olive" title="b2">F1</font> &amp; <font color="Olive" title="b4">F</font> <a href="cardfil2.html#R2" title="CARDFIL2:pred.2">is_filter-finer_than</a> <font color="Olive" title="b3">F2</font> holds <br/> for <font color="Olive" title="b5">M1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">F1</font><br/>  for <font color="Olive" title="b6">M2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b3">F2</font>  holds  not <font color="Olive" title="b5">M1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b6">M2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </div></div>
