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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="rewrite2.html#NM1" title="REWRITE2:NM.1">semi-Thue-system</a> of <font color="Maroon" title="c1">E</font><br/> for <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">t</font> being   <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>   st <font color="Olive" title="b1">S</font> is   <a href="rewrite2.html#NM2" title="REWRITE2:NM.2">Thue-system</a> of <font color="Maroon" title="c1">E</font> &amp; <font color="Olive" title="b2">s</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Olive" title="b3">t</font>,<font color="Olive" title="b1">S</font> holds <br/><font color="Olive" title="b3">t</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Olive" title="b2">s</font>,<font color="Olive" title="b1">S</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> being   <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>   st <font color="Maroon" title="c2">S</font> is   <a href="rewrite2.html#NM2" title="REWRITE2:NM.2">Thue-system</a> of <font color="Maroon" title="c1">E</font> &amp; <font color="Olive" title="b1">s</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Olive" title="b2">t</font>,<font color="Maroon" title="c2">S</font> holds <br/><font color="Olive" title="b2">t</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">S</font></span><br/><b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is   <a href="rewrite2.html#NM2" title="REWRITE2:NM.2">Thue-system</a> of <font color="Maroon" title="c1">E</font> &amp; <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> implies <font color="Maroon" title="c4">t</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c2">S</font> )</span><br/>







<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E17">A1</font></i>: 
( <font color="Maroon" title="c2">S</font> is   <a href="rewrite2.html#NM2" title="REWRITE2:NM.2">Thue-system</a> of <font color="Maroon" title="c1">E</font> &amp; <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">t</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c2">S</font></span><br/>

<a NAME="E2:34"/><b>then </b><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">S</font> <a href="relset_1.html#K6" title="RELSET_1:func.6">~</a> 
 
<b>by </b><i><a class="ref" href="relat_2.html#T30" title="RELAT_2:th.30">RELAT_2:30</a></i>;<br/>
<a NAME="E3:34"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="rewrite2.html#D4" target="_self" title="REWRITE2:def.4">Def4</a></i>;<br/>
<a NAME="E4:34"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c3">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="#E2:34"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="relat_1.html#D7" title="RELAT_1:def.7">RELAT_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E5:34"/>
<font color="Maroon" title="c4">t</font> <a href="rewrite2.html#R1" title="REWRITE2:pred.1">--&gt;.</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="rewrite2.html#D4" target="_self" title="REWRITE2:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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