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<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">t</font> be    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> ;<br/>





<b>assume </b><a NAME="E1:63"/>
<font color="Maroon" title="c2">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c3">t</font>, <a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span>
 ;<br/>

<a NAME="E2:63"/><b>then </b>
 <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <span class="p1">(<span class="default"><a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span></span>)</span> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>
 
<b>by </b><i><a class="ref" href="rewrite2.html#D7" target="_self" title="REWRITE2:def.7">Def7</a></i>;<br/>
<a NAME="E3:63"/><b>then </b>
 <a href="oposet_1.html#K1" title="OPOSET_1:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>
 
<b>by </b><i><a class="ref" href="rewrite2.html#T29" target="_self" title="REWRITE2:th.29">Th29</a></i>;<br/>
<a NAME="E4:63"/><b>then </b>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>
 
<b>by </b><i><a class="ref" href="oposet_1.html#D1" title="OPOSET_1:def.1">OPOSET_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:63"/>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T14" title="REWRITE1:th.14">REWRITE1:14</a></i>;<br/>


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