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<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="card_fin.html#D3" target="_self" title="CARD_FIN:def.3">CARD_FIN:def 3</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_2_1_1"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span> or  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_1"><b>suppose </b></a><a NAME="E1:47_2_1_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:47_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow20.html#D2" title="YELLOW20:def.2">YELLOW20:def 2</a></i>;<br/><a NAME="E3:47_2_1_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span>)</span> &amp; <font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 <b>by </b><i><a class="ref" href="yellow20.html#D2" title="YELLOW20:def.2">YELLOW20:def 2</a></i>;<br/><b>hence </b><a NAME="E4:47_2_1_1_1"/>
<span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_2_1_1_2"><b>suppose </b></a><a NAME="E1:47_2_1_1_2"/>
not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:47_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="yellow20.html#K1" title="YELLOW20:func.1">Intersect</a> <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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