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<b>let </b><font color="Maroon">s</font> be   <a href="turing_1.html#NM4">All-State</a> of <span class="p1">(<span class="default"><a href="turing_1.html#K18" target="_self">ZeroTuring</a>  <a href="turing_1.html#K32" target="_self">';'</a> <a href="turing_1.html#K16" target="_self">SuccTuring</a> </span>)</span>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="turing_1.html#NM2">Tape</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ;<br/><b>let </b><font color="Maroon">h</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:102"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">h</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span> &amp; <font color="Maroon">t</font> <a href="turing_1.html#R2" target="_self">storeData</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">h</font>,<font color="Maroon">n</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 ;<br/>

<b>reconsider </b><font color="Maroon">h1</font> = <font color="Maroon">h</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<b>set </b><font color="Maroon">s1</font> = <span class="p1"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span>;<br/>
<a NAME="E3:102"/><i><font color="Green">E31</font></i>: 
0 <a href="hidden.html#R1">=</a> the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:102"/><b>then </b><i><font color="Green">E32</font></i>: 
( <span class="p1"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span> is <a href="turing_1.html#V2" target="_self">Accept-Halt</a> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K7">`3</a>  <a href="turing_1.html#R2" target="_self">storeData</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">h</font>,0</span><a href="finseq_4.html#K2">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="turing_1.html#E9:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="turing_1.html#T14" target="_self">Th14</a></i>;<br/>
the <a href="turing_1.html#U1" target="_self">Symbols</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a>  = 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i/>
<br/>.= 
the <a href="turing_1.html#U1" target="_self">Symbols</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> 
<b>by </b><i/>
;<br/>
<b>then reconsider </b><font color="Maroon">t2</font> = <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K7">`3</a>  as   <a href="turing_1.html#NM2">Tape</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a>  ;<br/>
<a NAME="E7:102"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">t2</font> <a href="turing_1.html#R2" target="_self">storeData</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">h</font>,0</span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="turing_1.html#D9" target="_self">Def9</a>, <a class="ref" href="turing_1.html#T13" target="_self">Th13</a></i>;<br/>
<b>set </b><font color="Maroon">s2</font> = <span class="p1"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t2</font></span><a href="domain_1.html#K4">]</a></span>;<br/>
<a NAME="E8:102"/><i><font color="Green">E35</font></i>: 
0 <a href="hidden.html#R1">=</a> the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E9:102"/><b>then </b><i><font color="Green">E75</font></i>: 
( <span class="p1"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t2</font></span><a href="domain_1.html#K4">]</a></span> is <a href="turing_1.html#V2" target="_self">Accept-Halt</a> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t2</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t2</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K7">`3</a>  <a href="turing_1.html#R2" target="_self">storeData</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">h</font>,<span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="turing_1.html#D10" target="_self">Def10</a>, <a class="ref" href="turing_1.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E10:102"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <span class="p2">(<span class="default"><a href="turing_1.html#K18" target="_self">ZeroTuring</a>  <a href="turing_1.html#K32" target="_self">';'</a> <a href="turing_1.html#K16" target="_self">SuccTuring</a> </span>)</span>,<font color="Maroon">h</font>,<font color="Maroon">t</font></span><a href="domain_1.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="turing_1.html#E9:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="turing_1.html#T15" target="_self">Th15</a>, , </i>;<br/>
<b>hence </b><a NAME="E11:102"/>
<font color="Maroon">s</font> is <a href="turing_1.html#V2" target="_self">Accept-Halt</a>
 <b>by </b><i><a class="ref" href="turing_1.html#D9" target="_self">Def9</a>, , <a class="ref" href="turing_1.html#T12" target="_self">Th12</a></i>;<br/>

<a NAME="E12:102"/><i><font color="Green">E116</font></i>: 
( <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <font color="Maroon">s</font></span>)</span> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t2</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K6">`2</a>  &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <font color="Maroon">s</font></span>)</span> <a href="mcart_1.html#K7">`3</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default">the <a href="turing_1.html#U4" target="_self">InitS</a> of <a href="turing_1.html#K16" target="_self">SuccTuring</a> ,<font color="Maroon">h1</font>,<font color="Maroon">t2</font></span><a href="domain_1.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K7">`3</a>  )
 
<b>by </b><i><a class="ref" href="turing_1.html#D9" target="_self">Def9</a>, , , <a class="ref" href="turing_1.html#T12" target="_self">Th12</a></i>;<br/>
<b>thus </b><a NAME="E13:102"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <font color="Maroon">s</font></span>)</span> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">h</font>
 <b>by </b><i><a class="ref" href="turing_1.html#D9" target="_self">Def9</a>, , , <a class="ref" href="turing_1.html#T12" target="_self">Th12</a></i>;<br/>

<b>thus </b><a NAME="E14:102"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K11" target="_self">Result</a> <font color="Maroon">s</font></span>)</span> <a href="mcart_1.html#K7">`3</a>  <a href="turing_1.html#R2" target="_self">storeData</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">h</font>,1</span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i>, , <a class="ref" href="turing_1.html#T13" target="_self">Th13</a></i>;<br/>


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