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<b>set </b><font color="Maroon">N</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">G</font>,<font color="Olive">f</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">G</font> is    <a href="grcat_1.html#M2">Element</a> of  <a href="grcat_1.html#K19">GroupObjects</a> <font color="Maroon">UN</font>, <font color="Olive">f</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="funct_2.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> : verum </span>}</span> ;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b> <a href="modcat_1.html#R1" target="_self">GO</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">R</font>;<br/>
<a NAME="E1:16_1_1"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y1</font>, <font color="Olive">y2</font> being   <a href="hidden.html#M1">set</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y1</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y2</font>] holds <br/><font color="Olive">y1</font> <a href="hidden.html#R1">=</a> <font color="Olive">y2</font>
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:16_1_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> iff  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">G</font>,<font color="Olive">f</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">G</font> is    <a href="grcat_1.html#M2">Element</a> of  <a href="grcat_1.html#K19">GroupObjects</a> <font color="Maroon">UN</font>, <font color="Olive">f</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="funct_2.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> : verum </span>}</span>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>] ) )
 <b>from </b><i><a class="ref" href="tarski.html#S1">TARSKI:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">Y</font>
;<br/>

<b>thus </b><a NAME="E4:16_1_1"/>
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> iff  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">G</font>,<font color="Olive">f</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">G</font> is    <a href="grcat_1.html#M2">Element</a> of  <a href="grcat_1.html#K19">GroupObjects</a> <font color="Maroon">UN</font>, <font color="Olive">f</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="funct_2.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> : verum </span>}</span>  &amp;  <a href="modcat_1.html#R1" target="_self">GO</a> <font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Maroon">R</font> ) )
 <b>by </b><i/>;<br/>


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