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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">R</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/><b>let </b><font color="Maroon" title="c4">y</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:28"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_2.html#K3" title="RELSET_2:func.3">.:</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">Z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:28"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Z</font>
 <b>and </b><br/><a NAME="E4:28"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c5">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_2.html#K3" title="RELSET_2:func.3">.:</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:28"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c6">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="relset_2.html#K3" title="RELSET_2:func.3">.:</a> <font color="Maroon" title="c3">R</font></span>)</span>
 <b>and </b><br/><a NAME="E7:28"/><i><font color="Green" title="E17">A4</font></i>: 
<font color="Maroon" title="c6">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>and </b><br/><a NAME="E8:28"/><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c5">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_2.html#K3" title="RELSET_2:func.3">.:</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">X</font>
 <b>by </b><i><a class="txt" href="relset_2.html#E4:28"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E9:28"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <font color="Maroon" title="c6">X</font>
 
<b>by </b><i><a class="txt" href="relset_2.html#E3:28"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="relset_2.html#E6:28"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="relset_2.html#E8:28"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="relset_2.html#T19" target="_self" title="RELSET_2:th.19">Th19</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E11:28"/><i><font color="Green" title="E19">A6</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#D13" title="RELAT_1:def.13">RELAT_1:def 13</a></i>;<br/>
<a NAME="E12:28"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="relset_2.html#E7:28"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="relset_2.html#E11:28"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>hence </b><a NAME="E13:28"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> <a href="relat_1.html#K9" title="RELAT_1:func.9">.:</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="relset_2.html#E11:28"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="relat_1.html#D13" title="RELAT_1:def.13">RELAT_1:def 13</a></i>;<br/>


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