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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies  <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>  <a href="turing_1.html#R3" title="TURING_1:pred.3">computes</a> <font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> )</span><br/>

<span class="kw">assume </span><a NAME="E1:68"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ; <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">  <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>  <a href="turing_1.html#R3" title="TURING_1:pred.3">computes</a> <font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="68_1"><span class="kw">now </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">  for <font color="Olive" title="b1">s</font> being   <a href="turing_1.html#NM4" title="TURING_1:NM.4">All-State</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a><br/>  for <font color="Olive" title="b2">t</font> being   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a><br/>  for <font color="Olive" title="b3">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b4">x</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"> the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>,<font color="Olive" title="b3">h</font>,<font color="Olive" title="b2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Olive" title="b2">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b3">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b4">x</font> holds <br/>( <font color="Olive" title="b1">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp;  ex <font color="Olive" title="b5">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b6">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">h2</font> &amp; <font color="Olive" title="b6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b5">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b6">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) )</span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c2">cs</font> = <font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>;<br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="turing_1.html#NM4" title="TURING_1:NM.4">All-State</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</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">t</font> being   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a><br/>  for <font color="Olive" title="b2">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">x</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"> the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>,<font color="Olive" title="b2">h</font>,<font color="Olive" title="b1">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Olive" title="b1">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">x</font> holds <br/>( <font color="Maroon" title="c3">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp;  ex <font color="Olive" title="b4">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b5">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">h2</font> &amp; <font color="Olive" title="b5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b4">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b5">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">t</font> be   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</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">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">x</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"> the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>,<font color="Olive" title="b1">h</font>,<font color="Maroon" title="c4">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c4">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">x</font> holds <br/>( <font color="Maroon" title="c3">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp;  ex <font color="Olive" title="b3">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b4">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h2</font> &amp; <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b3">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b4">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">h</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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">x</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"> the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>,<font color="Maroon" title="c5">h</font>,<font color="Maroon" title="c4">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c4">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">x</font> holds <br/>( <font color="Maroon" title="c3">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp;  ex <font color="Olive" title="b2">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">h2</font> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b3">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"> the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>,<font color="Maroon" title="c5">h</font>,<font color="Maroon" title="c4">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c4">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c6">x</font> implies ( <font color="Maroon" title="c3">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp;  ex <font color="Olive" title="b1">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) ) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:68_1"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:68_1"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"> the <a href="turing_1.html#U4" title="TURING_1:sel.4">InitS</a> of <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>,<font color="Maroon" title="c5">h</font>,<font color="Maroon" title="c4">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E3:68_1"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c4">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c6">x</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="c3">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp;  ex <font color="Olive" title="b1">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) )</span><br/><a NAME="E4:68_1"/>
<font color="Maroon" title="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68_1"><span class="lab"><font color="Green" title="E47">A2</font></span></a></span>;<br/><a NAME="E5:68_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">f</font> where <font color="Olive" title="b1">f</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#D4" onmouseover="rs('finseq_2/D4')" onmouseout="rh()">FINSEQ_2:def 4</a></span>;<br/><a NAME="E6:68_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A6</font></span>: 
 ex <font color="Olive" title="b1">f</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 ;<br/><a NAME="E7:68_1"/><span class="lab"><font color="Green" title="E51">A7</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c5">h</font>,<font color="Maroon" title="c4">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68_1"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="turing_1.html#D19" target="_self" onmouseover="rs('turing_1/D19')" onmouseout="rh()">Def19</a></span>;<br/><span class="kw">hence </span><a NAME="E8:68_1"/>
<font color="Maroon" title="c3">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:68_1"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="txt" href="#E6:68_1"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="ref" href="turing_1.html#T34" target="_self" onmouseover="rs('turing_1/T34')" onmouseout="rh()">Th34</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">  ex <font color="Olive" title="b1">h2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ex <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h2</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )</span><br/><span class="kw">take </span><font color="Maroon" title="c7">h2</font> = <font color="Maroon" title="c5">h</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">  ex <font color="Olive" title="b1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  st <br/>( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font> &amp; <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )</span><br/><span class="kw">take </span><font color="Maroon" title="c8">y</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> ( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )</span><br/><span class="kw">thus </span><a NAME="E9:68_1"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:68_1"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="txt" href="#E6:68_1"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="txt" href="#E7:68_1"><span class="lab"><font color="Green" title="E51">A7</font></span></a>, <a class="ref" href="turing_1.html#T34" target="_self" onmouseover="rs('turing_1/T34')" onmouseout="rh()">Th34</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"> ( <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )</span><br/><span class="kw">thus </span><a NAME="E10:68_1"/>
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68_1"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</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"> <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><br/><a NAME="E11:68_1"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c7">h2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:68_1"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="txt" href="#E6:68_1"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="txt" href="#E7:68_1"><span class="lab"><font color="Green" title="E51">A7</font></span></a>, <a class="ref" href="turing_1.html#T34" target="_self" onmouseover="rs('turing_1/T34')" onmouseout="rh()">Th34</a></span>;<br/><span class="kw">hence </span><a NAME="E12:68_1"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c7">h2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:68"/>
 <a href="turing_1.html#K17" title="TURING_1:func.17">ZeroTuring</a>  <a href="turing_1.html#R3" title="TURING_1:pred.3">computes</a> <font color="Maroon" title="c1">n</font> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"> verum</span><br/>


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