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<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Ch</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">Fy</font> be  <a href="finset_1.html#V2">finite-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/>





<b>assume </b><a NAME="E1:48"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">Ch</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:48"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">Ch</font> &amp; <font color="Maroon">Ch</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:48"/>
<font color="Maroon">Ch</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:48"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Ch</font> <a href="relat_1.html#K10">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E6:48"/><b>then </b>
(  <a href="card_fin.html#K2" target="_self">Intersection</a> <font color="Maroon">Fy</font>,<font color="Maroon">Ch</font>,<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Fy</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">Fy</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is <a href="finset_1.html#V1">finite</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:48"/>
 <a href="card_fin.html#K2" target="_self">Intersection</a> <font color="Maroon">Fy</font>,<font color="Maroon">Ch</font>,<font color="Maroon">y</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>


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