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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: CARD_FIN:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">X</font>, <font color="Olive" title="b4">Y</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">Fy</font> being   <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b5">Fy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="funct_4.html#K6" title="FUNCT_4:func.6">--&gt;</a> (<font color="Olive" title="b3">X</font>,<font color="Olive" title="b4">Y</font>) holds <br/>(  <a href="card_fin.html#K3" title="CARD_FIN:func.3">Card_Intersection</a> (<font color="Olive" title="b5">Fy</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">X</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b4">Y</font></span>)</span> &amp;  <a href="card_fin.html#K3" title="CARD_FIN:func.3">Card_Intersection</a> (<font color="Olive" title="b5">Fy</font>,2) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b4">Y</font></span>)</span> )</div></div>
