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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^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/><span class="kw">let </span><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>







<span class="kw">assume </span><a NAME="E1:33"/>
( <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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E2:33"/><span class="kw">then </span>
( <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#K3" title="RELSET_1:func.3">~</a>  &amp; <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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#T13" onmouseover="rs('relat_2/T13')" onmouseout="rh()">RELAT_2:13</a></span>;<br/>
<a NAME="E3:33"/><span class="kw">then </span>
<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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D7" onmouseover="rs('relat_1/D7')" onmouseout="rh()">RELAT_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:33"/>
<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>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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