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<b>let </b><font color="Maroon" title="c1">P</font>, <font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c3">Q</font>, <font color="Maroon" title="c4">S</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/>







<b>assume </b><a NAME="E1:48"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c1">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">R</font> &amp; <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">S</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:48_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">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="c1">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">Q</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c7">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:48_1"/><i><font color="Green" title="E25">A2</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c7">z</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="c1">P</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c6">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">Q</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#D8" target="_self" title="RELAT_1:def.8">Def8</a></i>;<br/><b>thus </b><a NAME="E4:48_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">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">R</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">S</font>
 <b>by </b><i><a class="txt" href="relat_1.html#E1:48"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="relat_1.html#E3:48_1"><i><font color="Green" title="E25">A2</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>
<b>hence </b><a NAME="E3:48"/>
<font color="Maroon" title="c1">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c3">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">R</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">S</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D3" target="_self" title="RELAT_1:def.3">Def3</a></i>;<br/>


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