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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> 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="E1:33"/>
<font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 ;<br/>

<a NAME="E2:33"/><b>then </b>
<font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R2" title="REWRITE2:pred.2">==&gt;.</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="rewrite2.html#T10" target="_self" title="REWRITE2:th.10">Th10</a></i>;<br/>
<b>hence </b><a NAME="E3:33"/>
( <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#R2" title="REWRITE2:pred.2">==&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> &amp; <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#R2" title="REWRITE2:pred.2">==&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="ref" href="rewrite2.html#T12" target="_self" title="REWRITE2:th.12">Th12</a></i>;<br/>


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