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<b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>

<b>thus </b><a NAME="E1:25"/>
( <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font> <a href="dickson.html#K3" target="_self">\~</a>  implies <font color="Maroon">R</font> is <a href="relat_2.html#V5">asymmetric</a> )
 ;<br/>

<b>assume </b><a NAME="E2:25"/>
<font color="Maroon">R</font> is <a href="relat_2.html#V5">asymmetric</a>
 ;<br/>

<a NAME="E3:25"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">R</font> <a href="relat_2.html#R5">is_asymmetric_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D13">RELAT_2:def 13</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:25_1_1"/><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 ;<br/><a NAME="E2:25_1_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><a NAME="E3:25_1_1"/><b>then </b>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 <b>by </b><i>, , <a class="ref" href="relat_2.html#D5">RELAT_2:def 5</a></i>;<br/><a NAME="E4:25_1_1"/><b>then </b>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> <a href="relat_1.html#K4">~</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/><b>hence </b><a NAME="E5:25_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> <a href="dickson.html#K3" target="_self">\~</a> 
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:25_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> <a href="dickson.html#K3" target="_self">\~</a> 
 ;<br/><b>hence </b><a NAME="E3:25_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font> <a href="dickson.html#K3" target="_self">\~</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a></i>;<br/>


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