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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>, <font color="Maroon" title="c4">U</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="c5">w</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="E1:78"/>
(  <a href="rewrite2.html#K10" title="REWRITE2:func.10">Lang</a> <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rewrite2.html#K10" title="REWRITE2:func.10">Lang</a> <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c3">T</font> &amp;  <a href="rewrite2.html#K10" title="REWRITE2:func.10">Lang</a> <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rewrite2.html#K10" title="REWRITE2:func.10">Lang</a> <font color="Maroon" title="c5">w</font>,<font color="Maroon" title="c4">U</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite2.html#D9" target="_self" title="REWRITE2:def.9">REWRITE2:def 9</a><br/>

<b>hence </b><a NAME="E2:78"/>
<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c4">U</font> <a href="rewrite2.html#R4" title="REWRITE2:pred.4">are_equivalent_wrt</a> <font color="Maroon" title="c5">w</font>
 <b>by </b><i><a class="ref" href="rewrite2.html#D9" target="_self" title="REWRITE2:def.9">Def9</a></i>;<br/>


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