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<b>let </b><font color="Maroon" title="c1">s</font> be   <a href="turing_1.html#NM4" title="TURING_1:NM.4">All-State</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a> ;<br/><b>let </b><font color="Maroon" title="c2">t</font> be   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a> ;<br/><b>let </b><font color="Maroon" title="c3">h</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>







<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E54">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c1">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">0,<font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c2">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="c3">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="c4">f</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c5">m</font> = <font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1;<br/>
<b>set </b><font color="Maroon" title="c6">n</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/>
<a NAME="E2:68"/><i><font color="Green" title="E55">A2</font></i>: 
<font color="Maroon" title="c2">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c3">h</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="turing_1.html#T25" target="_self" title="TURING_1:th.25">Th25</a></i>;<br/>
<a NAME="E3:68"/><b>then </b><i><font color="Green" title="E56">A3</font></i>: 
( <font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c3">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 holds <br/><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )
 
<b>by </b><i><a class="ref" href="turing_1.html#D13" target="_self" title="TURING_1:def.13">Def13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">h1</font> = <font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<a NAME="E5:68"/><i><font color="Green" title="E57">A4</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">h1</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<a NAME="E6:68"/>
<font color="Maroon" title="c3">h</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E7:68"/><b>then </b><i><font color="Green" title="E58">A5</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E8:68"/>
<font color="Maroon" title="c7">h1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E9:68"/><b>then </b><i><font color="Green" title="E59">A6</font></i>: 
<font color="Maroon" title="c7">h1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="txt" href="turing_1.html#E7:68"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">s3</font> = <font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">F</font> = 0 as   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <b>by </b><i><a class="txt" href="turing_1.html#E70"><i><font color="Green" title="E51">Lm12</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">T</font> = 1 as   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <b>by </b><i><a class="txt" href="turing_1.html#E70"><i><font color="Green" title="E51">Lm12</font></i></a></i>;<br/>
<i><font color="Green" title="E60">A7</font></i>:  <a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font> = 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="turing_1.html#E3:68"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a>, <a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></i>
;<br/>
<i><font color="Green" title="E61">A8</font></i>:  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span> = 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">h</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">h</font>,<font color="Maroon" title="c9">F</font>
<b>by </b><i><a class="txt" href="turing_1.html#E13:68"><i><font color="Green" title="E60">A7</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<font color="Maroon" title="c2">t</font>
<b>by </b><i><a class="txt" href="turing_1.html#E3:68"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="turing_1.html#T28" target="_self" title="TURING_1:th.28">Th28</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c11">p1</font> = 1 as   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <b>by </b><i><a class="txt" href="turing_1.html#E69"><i><font color="Green" title="E50">Lm11</font></i></a></i>;<br/>
<a NAME="E16:68"/><i><font color="Green" title="E62">A9</font></i>: 
 <a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="turing_1.html#E13:68"><i><font color="Green" title="E60">A7</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>;<br/>
<b>set </b><font color="Maroon" title="c12">s1</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<i><font color="Green" title="E63">A10</font></i>:  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Maroon" title="c1">s</font> = 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="turing_1.html#E14:68"><i><font color="Green" title="E61">A8</font></i></a>, <a class="txt" href="turing_1.html#E71"><i><font color="Green" title="E52">Lm13</font></i></a></i>
<br/>.= 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E13:68"><i><font color="Green" title="E60">A7</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E1:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="turing_1.html#E16:68"><i><font color="Green" title="E62">A9</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c13">s13</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  ;<br/>
<b>set </b><font color="Maroon" title="c14">t1</font> =  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font>;<br/>
<a NAME="E19:68"/><i><font color="Green" title="E64">A11</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="turing_1.html#E3:68"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="turing_1.html#E5:68"><i><font color="Green" title="E57">A4</font></i></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<a NAME="E20:68"/><i><font color="Green" title="E65">A12</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<i><font color="Green" title="E66">A13</font></i>:  <a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> = 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">s13</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">s13</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,<span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">h1</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">2,1,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E2:68"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="turing_1.html#E5:68"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="turing_1.html#E9:68"><i><font color="Green" title="E59">A6</font></i></a>, <a class="ref" href="turing_1.html#D13" target="_self" title="TURING_1:def.13">Def13</a>, <a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></i>
;<br/>
<i><font color="Green" title="E67">A14</font></i>:  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span> = 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font>
<b>by </b><i><a class="txt" href="turing_1.html#E21:68"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
;<br/>
<a NAME="E23:68"/><i><font color="Green" title="E68">A15</font></i>: 
 <a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="turing_1.html#E21:68"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">p2</font> = 2 as   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <b>by </b><i><a class="txt" href="turing_1.html#E69"><i><font color="Green" title="E50">Lm11</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">i2</font> = <font color="Maroon" title="c7">h1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c17">s2</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<i><font color="Green" title="E69">A16</font></i>:  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> = 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E22:68"><i><font color="Green" title="E67">A14</font></i></a>, <a class="txt" href="turing_1.html#E71"><i><font color="Green" title="E52">Lm13</font></i></a></i>
<br/>.= 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E21:68"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E23:68"><i><font color="Green" title="E68">A15</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
;<br/>
<div><i><font color="Green" title="E70">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="68_7"><b>now </b></a><div class="add"><a NAME="E1:68_7"/><i><font color="Green" title="E71">A18</font></i>: 
the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 <b>by </b><i><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:68_7_1"/>
( <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span><b>by </b><i><a class="txt" href="turing_1.html#E1:68_7"><i><font color="Green" title="E71">A18</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_7_1_1"><b>suppose </b></a><a NAME="E1:68_7_1_1"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:68_7_1_1"/>
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">3,0,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_7_1_2"><b>suppose </b></a><a NAME="E1:68_7_1_2"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:68_7_1_2"/>
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <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">3,0,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>reconsider </b><font color="Maroon" title="c18">s23</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  ;<br/>
<i><font color="Green" title="E71">A19</font></i>:  <a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> = 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">s23</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">s23</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">3,0,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E27:68"><i><font color="Green" title="E70">A17</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
;<br/>
<b>set </b><font color="Maroon" title="c19">t2</font> =  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font>;<br/>
<i><font color="Green" title="E72">A20</font></i>:  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span> = 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font>
<b>by </b><i><a class="txt" href="turing_1.html#E29:68"><i><font color="Green" title="E71">A19</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
;<br/>
<a NAME="E31:68"/><i><font color="Green" title="E73">A21</font></i>: 
<font color="Maroon" title="c7">h1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c16">i2</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<a NAME="E32:68"/><b>then </b><i><font color="Green" title="E74">A22</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="turing_1.html#E5:68"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="turing_1.html#E19:68"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<a NAME="E33:68"/><i><font color="Green" title="E75">A23</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="turing_1.html#E20:68"><i><font color="Green" title="E65">A12</font></i></a>, <a class="txt" href="turing_1.html#E31:68"><i><font color="Green" title="E73">A21</font></i></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<a NAME="E34:68"/><i><font color="Green" title="E76">A24</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<a NAME="E35:68"/><i><font color="Green" title="E77">A25</font></i>: 
 <a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
 
<b>by </b><i><a class="txt" href="turing_1.html#E29:68"><i><font color="Green" title="E71">A19</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>;<br/>
<a NAME="E36:68"/><i><font color="Green" title="E78">A26</font></i>: 
<font color="Maroon" title="c16">i2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h1</font>
 
;<br/>
<b>reconsider </b><font color="Maroon" title="c20">p3</font> = 3 as   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <b>by </b><i><a class="txt" href="turing_1.html#E69"><i><font color="Green" title="E50">Lm11</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c21">s3</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<i><font color="Green" title="E79">A27</font></i>:  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> = 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E30:68"><i><font color="Green" title="E72">A20</font></i></a>, <a class="txt" href="turing_1.html#E71"><i><font color="Green" title="E52">Lm13</font></i></a></i>
<br/>.= 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">3,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">i2</font>,<span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E29:68"><i><font color="Green" title="E71">A19</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E35:68"><i><font color="Green" title="E77">A25</font></i></a>, <a class="txt" href="turing_1.html#E36:68"><i><font color="Green" title="E78">A26</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c22">s33</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  ;<br/>
<i><font color="Green" title="E80">A28</font></i>:  <a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> = 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c22">s33</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c22">s33</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<a href="turing_1.html#K17" title="TURING_1:func.17">Zero_Tran</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">4,1,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E33:68"><i><font color="Green" title="E75">A23</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a>, <a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c23">t3</font> =  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font>;<br/>
<a NAME="E41:68"/><i><font color="Green" title="E81">A29</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="turing_1.html#E5:68"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="turing_1.html#E32:68"><i><font color="Green" title="E74">A22</font></i></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<a NAME="E42:68"/><i><font color="Green" title="E82">A30</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<a NAME="E43:68"/><i><font color="Green" title="E83">A31</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="turing_1.html#E31:68"><i><font color="Green" title="E73">A21</font></i></a>, <a class="txt" href="turing_1.html#E34:68"><i><font color="Green" title="E76">A24</font></i></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></i>;<br/>
<i><font color="Green" title="E84">A32</font></i>:  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span> = 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font>
<b>by </b><i><a class="txt" href="turing_1.html#E40:68"><i><font color="Green" title="E80">A28</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
;<br/>
<a NAME="E45:68"/><i><font color="Green" title="E85">A33</font></i>: 
 <a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c20">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
 
<b>by </b><i><a class="txt" href="turing_1.html#E40:68"><i><font color="Green" title="E80">A28</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>;<br/>
<a NAME="E46:68"/><i><font color="Green" title="E86">A34</font></i>: 
<font color="Maroon" title="c7">h1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font>
 
;<br/>
<b>reconsider </b><font color="Maroon" title="c24">p3</font> = 3 as   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a>  <b>by </b><i><a class="txt" href="turing_1.html#E69"><i><font color="Green" title="E50">Lm11</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c25">s3</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<i><font color="Green" title="E87">A35</font></i>:  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> = 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E44:68"><i><font color="Green" title="E84">A32</font></i></a>, <a class="txt" href="turing_1.html#E71"><i><font color="Green" title="E52">Lm13</font></i></a></i>
<br/>.= 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">4,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">Head</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p5">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c24">p3</font>,<font color="Maroon" title="c7">h1</font>,<span class="p0">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E40:68"><i><font color="Green" title="E80">A28</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">4,<font color="Maroon" title="c3">h</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E45:68"><i><font color="Green" title="E85">A33</font></i></a>, <a class="txt" href="turing_1.html#E46:68"><i><font color="Green" title="E86">A34</font></i></a>, <a class="txt" href="turing_1.html#E45"><i><font color="Green" title="E32">Lm4</font></i></a></i>
;<br/>
<b>set </b><font color="Maroon" title="c26">Rs</font> = <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<i><font color="Green" title="E88">A36</font></i>: <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="turing_1.html#D8" target="_self" title="TURING_1:def.8">Def8</a></i>
<br/>.= 
 <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="turing_1.html#D8" target="_self" title="TURING_1:def.8">Def8</a></i>
<br/>.= 
 <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="turing_1.html#D8" target="_self" title="TURING_1:def.8">Def8</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">4,<font color="Maroon" title="c3">h</font>,<span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p4">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="turing_1.html#E17:68"><i><font color="Green" title="E63">A10</font></i></a>, <a class="txt" href="turing_1.html#E26:68"><i><font color="Green" title="E69">A16</font></i></a>, <a class="txt" href="turing_1.html#E38:68"><i><font color="Green" title="E79">A27</font></i></a>, <a class="txt" href="turing_1.html#E48:68"><i><font color="Green" title="E87">A35</font></i></a>, <a class="ref" href="turing_1.html#T12" target="_self" title="TURING_1:th.12">Th12</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E89">A37</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  = 
4
<b>by </b><i><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>
<br/>.= 
the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a> 
<b>by </b><i><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></i>
;<br/>
<b>hence </b><a NAME="E51:68"/>
<font color="Maroon" title="c1">s</font> is <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>
 <b>by </b><i><a class="ref" href="turing_1.html#D9" target="_self" title="TURING_1:def.9">Def9</a></i>;<br/>

<a NAME="E52:68"/><b>then </b><i><font color="Green" title="E90">A38</font></i>: 
 <a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="turing_1.html#E50:68"><i><font color="Green" title="E89">A37</font></i></a>, <a class="ref" href="turing_1.html#D10" target="_self" title="TURING_1:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E53:68"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="turing_1.html#E49:68"><i><font color="Green" title="E88">A36</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>;<br/>

<a NAME="E54:68"/><i><font color="Green" title="E91">A39</font></i>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font>
 
<b>by </b><i><a class="txt" href="turing_1.html#E49:68"><i><font color="Green" title="E88">A36</font></i></a>, <a class="txt" href="turing_1.html#E52:68"><i><font color="Green" title="E90">A38</font></i></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></i>;<br/>
<a NAME="E55:68"/><i><font color="Green" title="E92">A40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_16"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c27">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>assume </b><a NAME="E1:68_16"/><i><font color="Green" title="E93">A41</font></i>: 
( <font color="Maroon" title="c3">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c27">k</font> &amp; <font color="Maroon" title="c27">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 )
 ;<br/><a NAME="E2:68_16"/><b>then </b><i><font color="Green" title="E94">A42</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c27">k</font>
 <b>by </b><i><a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><a NAME="E3:68_16"/>
<font color="Maroon" title="c27">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="turing_1.html#E55:68"><i><font color="Green" title="E92">A40</font></i></a>, <a class="txt" href="turing_1.html#E1:68_16"><i><font color="Green" title="E93">A41</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><b>hence </b><a NAME="E4:68_16"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p3">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="turing_1.html#E42:68"><i><font color="Green" title="E82">A30</font></i></a>, <a class="txt" href="turing_1.html#E2:68_16"><i><font color="Green" title="E94">A42</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E57:68"/><b>then </b>
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p2">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font></span>)</span>,<font color="Maroon" title="c16">i2</font>,<font color="Maroon" title="c9">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c10">T</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c3">h</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<b>by </b><i><a class="txt" href="turing_1.html#E41:68"><i><font color="Green" title="E81">A29</font></i></a>, <a class="txt" href="turing_1.html#E43:68"><i><font color="Green" title="E83">A31</font></i></a>, <a class="ref" href="turing_1.html#D13" target="_self" title="TURING_1:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E58:68"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="mcart_1.html#K7" title="MCART_1:func.7">`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="c3">h</font>,0</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="turing_1.html#E54:68"><i><font color="Green" title="E91">A39</font></i></a>, <a class="ref" href="turing_1.html#T19" target="_self" title="TURING_1:th.19">Th19</a></i>;<br/>


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