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<b>let </b><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="E1:71"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be   <a href="turing_1.html#NM4">All-State</a> of <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ;<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> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>set </b><font color="Maroon">cs</font> = <font color="Maroon">n</font> <a href="comput_1.html#K6">const</a> 0;<br/><b>assume </b><a NAME="E1:71_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K6">const</a> 0</span>)</span> &amp; <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 <a href="turing_1.html#K18" target="_self">ZeroTuring</a> ,<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_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">h</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font> )
 ;<br/><a NAME="E2:71_1"/>
 <a href="comput_1.html#K3">arity</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K6">const</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="comput_1.html#T35">COMPUT_1:35</a></i>;<br/><a NAME="E3:71_1"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K6">const</a> 0</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="comput_1.html#T24">COMPUT_1:24</a></i>;<br/><a NAME="E4:71_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="turing_1.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E5:71_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/><b>then consider </b><font color="Maroon">f</font> being    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K5">NAT</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E7:71_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/><a NAME="E8:71_1"/><i><font color="Green">E35</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">0,<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="ref" href="turing_1.html#T7" target="_self">Th7</a>, </i>;<br/><b>hence </b><a NAME="E9:71_1"/>
<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#T6" target="_self">Th6</a>, <a class="ref" href="turing_1.html#T7" target="_self">Th7</a>, , <a class="ref" href="turing_1.html#T5" target="_self">Th5</a></i>;<br/><b>take </b><font color="Maroon">h2</font> = <font color="Maroon">h</font>;<br/><b>take </b><font color="Maroon">y</font> = 0;<br/><b>thus </b><a NAME="E10:71_1"/>
<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">h2</font>
 <b>by </b><i><a class="ref" href="turing_1.html#T6" target="_self">Th6</a>, <a class="ref" href="turing_1.html#T7" target="_self">Th7</a>, , , <a class="ref" href="turing_1.html#T5" target="_self">Th5</a></i>;<br/><b>thus </b><a NAME="E11:71_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K6">const</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="turing_1.html#T7" target="_self">Th7</a>, , <a class="ref" href="comput_1.html#T36">COMPUT_1:36</a></i>;<br/><a NAME="E12:71_1"/>
<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">h2</font>,0</span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="turing_1.html#T6" target="_self">Th6</a>, <a class="ref" href="turing_1.html#T7" target="_self">Th7</a>, , , <a class="ref" href="turing_1.html#T5" target="_self">Th5</a></i>;<br/><b>hence </b><a NAME="E13:71_1"/>
<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_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">h2</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">y</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D9">FINSEQ_1:def 9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:71"/>
 <a href="turing_1.html#K18" target="_self">ZeroTuring</a>  <a href="turing_1.html#R3" target="_self">computes</a> <font color="Maroon">n</font> <a href="comput_1.html#K6">const</a> 0
 <b>by </b><i/>;<br/>


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