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<span class="kw">reconsider </span><font color="Maroon" title="c4">l</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E2:89_1_2"/>
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span>,<font color="Maroon" title="c4">l</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K20" title="TURING_1:func.20">UnionSt</a> (<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)</span>)</span>,<span class="p2">(<span class="default"> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:89_1_2"/>
( (  ex <font color="Olive" title="b1">p</font> being   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <font color="Maroon" title="c1">s</font> ex <font color="Olive" title="b2">y</font> being   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <font color="Maroon" title="c1">s</font> st <br/>( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">p</font>, the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">s</font> ) implies  <a href="turing_1.html#K21" title="TURING_1:func.21">FirstTuringTran</a> (<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<span class="p1">(<span class="default"> the <a href="turing_1.html#U3" title="TURING_1:sel.3">Tran</a> of <font color="Maroon" title="c1">s</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K25" title="TURING_1:func.25">FirstTuringState</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K27" title="TURING_1:func.27">FirstTuringSymbol</a> <font color="Maroon" title="c3">x</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K20" title="TURING_1:func.20">UnionSt</a> (<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)</span>)</span>,<span class="p2">(<span class="default"> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> ) &amp; (  ex <font color="Olive" title="b1">q</font> being   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <font color="Maroon" title="c2">t</font> ex <font color="Olive" title="b2">y</font> being   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <font color="Maroon" title="c2">t</font> st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"> the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">s</font>,<font color="Olive" title="b1">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> implies  <a href="turing_1.html#K22" title="TURING_1:func.22">SecondTuringTran</a> (<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<span class="p1">(<span class="default"> the <a href="turing_1.html#U3" title="TURING_1:sel.3">Tran</a> of <font color="Maroon" title="c2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K26" title="TURING_1:func.26">SecondTuringState</a> <font color="Maroon" title="c3">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="turing_1.html#K28" title="TURING_1:func.28">SecondTuringSymbol</a> <font color="Maroon" title="c3">x</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span>) is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K20" title="TURING_1:func.20">UnionSt</a> (<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)</span>)</span>,<span class="p2">(<span class="default"> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> ) &amp; ( (  for <font color="Olive" title="b1">p</font> being   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <font color="Maroon" title="c1">s</font><br/>  for <font color="Olive" title="b2">y</font> being   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <font color="Maroon" title="c1">s</font>  holds <br/>(  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">p</font>, the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or  not <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">s</font> ) ) &amp; (  for <font color="Olive" title="b1">q</font> being   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <font color="Maroon" title="c2">t</font><br/>  for <font color="Olive" title="b2">y</font> being   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <font color="Maroon" title="c2">t</font>  holds  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"> the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <font color="Maroon" title="c1">s</font>,<font color="Olive" title="b1">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> ) implies <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K20" title="TURING_1:func.20">UnionSt</a> (<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)</span>)</span>,<span class="p2">(<span class="default"> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> ) )
 ; <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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