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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">P</font>, <font color="Maroon" title="c3">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><i><font color="Green" title="E51">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:106_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font>
 ;<br/><a NAME="E2:106_1_1"/><b>then </b><i><font color="Green" title="E52">A2</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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="c2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#D11" target="_self" title="RELAT_1:def.11">Def11</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:106_1_1"/><i><font color="Green" title="E53">A3</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">a</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="c2">P</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">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> )
 <b>by </b><i><a class="ref" href="relat_1.html#D8" target="_self" title="RELAT_1:def.8">Def8</a></i>;<br/><a NAME="E5:106_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">a</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="c2">P</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="relat_1.html#E2:106_1_1"><i><font color="Green" title="E52">A2</font></i></a>, <a class="txt" href="relat_1.html#E4:106_1_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="relat_1.html#D11" target="_self" title="RELAT_1:def.11">Def11</a></i>;<br/><b>hence </b><a NAME="E6:106_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="txt" href="relat_1.html#E4:106_1_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="relat_1.html#D8" target="_self" title="RELAT_1:def.8">Def8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:106_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:106_1_2"/><i><font color="Green" title="E52">A4</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">a</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="c2">P</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">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> )
 <b>by </b><i><a class="ref" href="relat_1.html#D8" target="_self" title="RELAT_1:def.8">Def8</a></i>;<br/><a NAME="E4:106_1_2"/><i><font color="Green" title="E53">A5</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">a</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="c2">P</font> )
 <b>by </b><i><a class="txt" href="relat_1.html#E3:106_1_2"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="relat_1.html#D11" target="_self" title="RELAT_1:def.11">Def11</a></i>;<br/><a NAME="E5:106_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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="c2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="txt" href="relat_1.html#E3:106_1_2"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="relat_1.html#D8" target="_self" title="RELAT_1:def.8">Def8</a></i>;<br/><b>hence </b><a NAME="E6:106_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="relat_1.html#E4:106_1_2"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="relat_1.html#D11" target="_self" title="RELAT_1:def.11">Def11</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:106_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font> )
 <b>by </b><i><a class="txt" href="relat_1.html#E1:106_1"><i><font color="Green" title="E51">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:106"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D2" target="_self" title="RELAT_1:def.2">Def2</a></i>;<br/>


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