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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th12</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: CARDFIL2:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</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="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font><br/>  for <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><br/>  for <font color="Olive" title="b5">B</font> being   <a href="cardfil2.html#NM1" title="CARDFIL2:NM.1">basis</a> of <font color="Olive" title="b4">F</font> holds <br/> ( <font color="Olive" title="b3">f</font> <a href="funct_2.html#K7" title="FUNCT_2:func.7">.:</a> <span class="p1">(<span class="default"><a href="cardfil2.html#K4" title="CARDFIL2:func.4">#</a> <font color="Olive" title="b5">B</font></span>)</span> is   <a href="cardfil2.html#NM2" title="CARDFIL2:NM.2">filter_base</a> of <font color="Olive" title="b2">Y</font> &amp; <span class="p1"><a href="cardfil2.html#K3" title="CARDFIL2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K7" title="FUNCT_2:func.7">.:</a> <span class="p3">(<span class="default"><a href="cardfil2.html#K4" title="CARDFIL2:func.4">#</a> <font color="Olive" title="b5">B</font></span>)</span></span>)</span></span><a href="cardfil2.html#K3" title="CARDFIL2:func.3">.]</a></span> is    <a href="card_fil.html#M1" title="CARD_FIL:mode.1">Filter</a> of <font color="Olive" title="b2">Y</font> &amp; <span class="p1"><a href="cardfil2.html#K3" title="CARDFIL2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K7" title="FUNCT_2:func.7">.:</a> <span class="p3">(<span class="default"><a href="cardfil2.html#K4" title="CARDFIL2:func.4">#</a> <font color="Olive" title="b5">B</font></span>)</span></span>)</span></span><a href="cardfil2.html#K3" title="CARDFIL2:func.3">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">M</font> where <font color="Olive" title="b6">M</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b2">Y</font> : <font color="Olive" title="b3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b6">M</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">F</font> </span> } </span>  )</div></div>
