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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> be   <a href="rewrite2.html#NM1" title="REWRITE2:NM.1">semi-Thue-system</a> of <font color="Maroon" title="c1">E</font>;<br/><b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font>, <font color="Maroon" title="c5">u</font>, <font color="Maroon" title="c6">v</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="E1:60"/><i><font color="Green" title="E38">A</font></i>: 
( <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c2">S</font> )
 ;<br/>

<a NAME="E2:60"/><i><font color="Green" title="E39">B1</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="rewrite2.html#E1:60"><i><font color="Green" title="E38">A</font></i></a>, <a class="ref" href="rewrite2.html#T36" target="_self" title="REWRITE2:th.36">ThDerivN50</a></i>;<br/>
<a NAME="E3:60"/>
<font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="rewrite2.html#E1:60"><i><font color="Green" title="E38">A</font></i></a>, <a class="ref" href="rewrite2.html#T36" target="_self" title="REWRITE2:th.36">ThDerivN50</a></i>;<br/>
<b>hence </b><a NAME="E4:60"/>
<font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="rewrite2.html#E2:60"><i><font color="Green" title="E39">B1</font></i></a>, <a class="ref" href="rewrite2.html#T35" target="_self" title="REWRITE2:th.35">ThDerivN40</a></i>;<br/>

<a NAME="E5:60"/><i><font color="Green" title="E40">B2</font></i>: 
<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="rewrite2.html#E1:60"><i><font color="Green" title="E38">A</font></i></a>, <a class="ref" href="rewrite2.html#T36" target="_self" title="REWRITE2:th.36">ThDerivN50</a></i>;<br/>
<a NAME="E6:60"/>
<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c6">v</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="rewrite2.html#E1:60"><i><font color="Green" title="E38">A</font></i></a>, <a class="ref" href="rewrite2.html#T36" target="_self" title="REWRITE2:th.36">ThDerivN50</a></i>;<br/>
<b>hence </b><a NAME="E7:60"/>
<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c6">v</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="rewrite2.html#E5:60"><i><font color="Green" title="E40">B2</font></i></a>, <a class="ref" href="rewrite2.html#T35" target="_self" title="REWRITE2:th.35">ThDerivN40</a></i>;<br/>


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