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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: CARD_FIN:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">Ch</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st ( <font color="Olive" title="b2">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">F</font></span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  ) holds <br/> <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">Ch</font>,<font color="Olive" title="b1">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b2">F</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T38" onmouseover="rs('relat_1/T38')" onmouseout="rh()">RELAT_1:38</a>, <a class="ref" href="zfmisc_1.html#T2" onmouseover="rs('zfmisc_1/T2')" onmouseout="rh()">ZFMISC_1:2</a></span>;<br/></div></div>
