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



<b>assume </b><a NAME="E1:5"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y</font>
 ;<br/>

<a NAME="E2:5"/><b>then </b>
<font color="Maroon" title="c2">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T131" title="RELAT_1:th.131">RELAT_1:131</a></i>;<br/>
<a NAME="E3:5"/><b>then </b><i><font color="Green" title="E3">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T105" title="RELAT_1:th.105">RELAT_1:105</a></i>;<br/>
<a NAME="E4:5"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="txt" href="yellow_2.html#E1:5"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="relat_1.html#T104" title="RELAT_1:th.104">RELAT_1:104</a></i>;<br/>
<a NAME="E5:5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="txt" href="yellow_2.html#E3:5"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:5"/><b>then </b>
<font color="Maroon" title="c1">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Y</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">|</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="ref" href="wellord1.html#T17" title="WELLORD1:th.17">WELLORD1:17</a></i>;<br/>
<b>hence </b><a NAME="E7:5"/>
<font color="Maroon" title="c1">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="ref" href="wellord1.html#T17" title="WELLORD1:th.17">WELLORD1:17</a></i>;<br/>


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