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<b>let </b><font color="Maroon">X'</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="funct_1.html#NM1">Function</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">z</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>









<b>assume </b><a NAME="E1:34"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="card_fin.html#K2" target="_self">Intersection</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span>,<font color="Maroon">Ch</font>,<font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:34"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T99">RELAT_1:99</a></i>;<br/>
<a NAME="E3:34"/><b>then </b><i><font color="Green">E50</font></i>: 
(  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font></span>)</span> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T95">ZFMISC_1:95</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:34_1"/><i><font color="Green">E51</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> )
 ;<br/><a NAME="E2:34_1"/>
<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="E3:34_1"/><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> &amp; <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> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span> )
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/><a NAME="E4:34_1"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X'</font></span>)</span> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:34_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:34"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="card_fin.html#K2" target="_self">Intersection</a> <font color="Maroon">F</font>,<font color="Maroon">Ch</font>,<font color="Maroon">y</font>
 <b>by </b><i>, </i>;<br/>


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