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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">Y1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be    <a href="relset_1.html#M2" target="_self">Relation</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/>







<b>assume </b><a NAME="E1:37"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y1</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_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>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1_1"/><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 ;<br/><a NAME="E2:37_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>hence </b><a NAME="E3:37_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> <a href="relset_1.html#K9" target="_self">|</a> <font color="Maroon">R</font>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#D12">RELAT_1:def 12</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E2:37_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> <a href="relset_1.html#K9" target="_self">|</a> <font color="Maroon">R</font> iff <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#D12">RELAT_1:def 12</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:37"/>
<font color="Maroon">Y1</font> <a href="relset_1.html#K9" target="_self">|</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a></i>;<br/>


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