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<span class="kw">reconsider </span><font color="Maroon" title="c1">F</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E67"><span class="lab"><font color="Green" title="E47">Lm9</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K18" title="TURING_1:func.18">ZeroTuring</a> <br/> for <font color="Olive" title="b2">head</font> being   <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/> for <font color="Olive" title="b3">f</font> being   <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>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Olive" title="b2">head</font>,<font color="Olive" title="b1">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Olive" title="b1">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">head</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">f</font> holds <br/>( <font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="Olive" title="b2">head</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="Olive" title="b2">head</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">head</font> being   <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/> for <font color="Olive" title="b2">f</font> being   <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>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Olive" title="b1">head</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c3">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">head</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">f</font> holds <br/>( <font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="Olive" title="b1">head</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="Olive" title="b1">head</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <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>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c3">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="c4">h</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">f</font> holds <br/>( <font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c3">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="c4">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="c5">f</font> implies ( <font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:73"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">and </span><br/><a NAME="E3:73"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:73"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
<font color="Maroon" title="c3">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="c4">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="c5">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a>  &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">s3</font> = <font color="Maroon" title="c2">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/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">h1</font> = <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1: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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">m</font> = <font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">n</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2;<br/>
<a NAME="E7:73"/><span class="lab"><font color="Green" title="E53">A4</font></span>: 
<font color="Maroon" title="c4">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">h1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E66"><span class="lab"><font color="Green" title="E46">Lm8</font></span></a></span>;<br/>
<a NAME="E9:73"/><span class="lab"><font color="Green" title="E54">A5</font></span>: 
<font color="Maroon" title="c7">h1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</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="c4">h</font>
 
;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">s1</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">i2</font> = <font color="Maroon" title="c7">h1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></span>;<br/>
<a NAME="E11:73"/><span class="lab"><font color="Green" title="E55">A6</font></span>: 
<font color="Maroon" title="c7">h1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">i2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E67"><span class="lab"><font color="Green" title="E47">Lm9</font></span></a></span>;<br/>
<a NAME="E13:73"/><span class="lab"><font color="Green" title="E56">A7</font></span>: 
<font color="Maroon" title="c12">i2</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</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/>
<span class="kw">set </span><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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font>;<br/>
<a NAME="E14:73"/><span class="lab"><font color="Green" title="E57">A8</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c4">h</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E4:73"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="turing_1.html#T25" target="_self" title="TURING_1:th.25">Th25</a></span>;<br/>
<a NAME="E15:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A9</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D13" target="_self" title="TURING_1:def.13">Def13</a></span>;<br/>
<a NAME="E16:73"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<a NAME="E17:73"/><span class="kw">then </span>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E11:73"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<a NAME="E18:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A10</font></span>: 
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<span class="lab"><font color="Green" title="E60">A11</font></span>:  <a href="turing_1.html#K8" title="TURING_1:func.8">TRAN</a> <font color="Maroon" title="c2">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="c2">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="c6">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="c2">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></span>
<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><font color="Maroon" title="c6">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="c2">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><font color="Maroon" title="c3">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="c2">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E15:73"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<a NAME="E20:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A12</font></span>: 
 <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="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">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="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E66"><span class="lab"><font color="Green" title="E46">Lm8</font></span></a></span>;<br/>
<a NAME="E22:73"/><span class="lab"><font color="Green" title="E62">A13</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
;<br/>
<a NAME="E23:73"/><span class="lab"><font color="Green" title="E63">A14</font></span>: 
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E64">A15</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="73_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c19">k</font> &amp; <font color="Maroon" title="c19">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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 implies <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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">assume </span><a NAME="E1:73_2"/>
( <font color="Maroon" title="c4">h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c19">k</font> &amp; <font color="Maroon" title="c19">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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E2:73_2"/><span class="kw">then </span>
( <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c19">k</font> &amp; <font color="Maroon" title="c19">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:73"><span class="lab"><font color="Green" title="E62">A13</font></span></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></span>;<br/><span class="kw">hence </span><a NAME="E3:73_2"/>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:73"><span class="lab"><font color="Green" title="E63">A14</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E25:73"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<a NAME="E26:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A16</font></span>: 
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:73"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">s3</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">s33</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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/>
<span class="lab"><font color="Green" title="E66">A17</font></span>:  <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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c20">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></span>
<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="c18">p3</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c20">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:73"><span class="lab"><font color="Green" title="E65">A16</font></span></a>, <a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<a NAME="E29:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A18</font></span>: 
 <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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E66"><span class="lab"><font color="Green" title="E46">Lm8</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c22">s13</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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/>
<a NAME="E32:73"/>
<font color="Maroon" title="c4">h</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E33:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A19</font></span>: 
<font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E34:73"/>
<font color="Maroon" title="c7">h1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></span>;<br/>
<a NAME="E35:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A20</font></span>: 
<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="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:73"><span class="lab"><font color="Green" title="E68">A19</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<span class="lab"><font color="Green" title="E70">A21</font></span>:  <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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c22">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></span>
<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="c10">p1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c22">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c10">p1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:73"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E7:73"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="txt" href="#E35:73"><span class="lab"><font color="Green" title="E69">A20</font></span></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></span>
;<br/>
<a NAME="E37:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A22</font></span>: 
 <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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E72">A23</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="73_5"><span class="kw">now </span></a><div class="add"><a NAME="E1:73_5"/><span class="lab"><font color="Green" title="E73">A24</font></span>: 
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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_5_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:73_5_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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73_5"><span class="lab"><font color="Green" title="E73">A24</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_5_1_1"><span class="kw">suppose </span></a><a NAME="E1:73_5_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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">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,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:73_5_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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">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,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_5_1_2"><span class="kw">suppose </span></a><a NAME="E1:73_5_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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">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,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:73_5_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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">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,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T38" target="_self" title="TURING_1:th.38">Th38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c23">s2</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">s23</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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/>
<span class="lab"><font color="Green" title="E73">A25</font></span>:  <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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c24">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></span>
<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="c21">p2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c24">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c21">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">3,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:73"><span class="lab"><font color="Green" title="E72">A23</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<a NAME="E41:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A26</font></span>: 
 <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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
 <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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:73"><span class="lab"><font color="Green" title="E73">A25</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E75">A27</font></span>:  <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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E68"><span class="lab"><font color="Green" title="E48">Lm10</font></span></a></span>
<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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:73"><span class="lab"><font color="Green" title="E73">A25</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:73"><span class="lab"><font color="Green" title="E74">A26</font></span></a>, <a class="txt" href="#E13:73"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c25">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E66"><span class="lab"><font color="Green" title="E46">Lm8</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E76">A28</font></span>:  <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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c18">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:73"><span class="lab"><font color="Green" title="E66">A17</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<span class="kw">set </span><font color="Maroon" title="c26">s3</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<span class="lab"><font color="Green" title="E77">A29</font></span>:  <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="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:73"><span class="lab"><font color="Green" title="E76">A28</font></span></a>, <a class="txt" href="turing_1.html#E68"><span class="lab"><font color="Green" title="E48">Lm10</font></span></a></span>
<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="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c25">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:73"><span class="lab"><font color="Green" title="E66">A17</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">4,<font color="Maroon" title="c4">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:73"><span class="lab"><font color="Green" title="E67">A18</font></span></a>, <a class="txt" href="#E9:73"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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="c2">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="c2">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="c3">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="c2">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="c2">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c4">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="c2">s</font></span>)</span> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c4">h</font>,<font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:73"><span class="lab"><font color="Green" title="E60">A11</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<font color="Maroon" title="c3">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:73"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="ref" href="turing_1.html#T28" target="_self" title="TURING_1:th.28">Th28</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E78">A30</font></span>:  <a href="turing_1.html#K9" title="TURING_1:func.9">Following</a> <font color="Maroon" title="c2">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="c2">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="c2">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="c2">s</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="turing_1.html#E68"><span class="lab"><font color="Green" title="E48">Lm10</font></span></a></span>
<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="c2">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="c2">s</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">t</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:73"><span class="lab"><font color="Green" title="E60">A11</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E20:73"><span class="lab"><font color="Green" title="E61">A12</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
 <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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
 <a href="turing_1.html#K5" title="TURING_1:func.5">Tape-Chg</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:73"><span class="lab"><font color="Green" title="E70">A21</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E79">A31</font></span>:  <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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E68"><span class="lab"><font color="Green" title="E48">Lm10</font></span></a></span>
<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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c10">p1</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c3">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:73"><span class="lab"><font color="Green" title="E70">A21</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c21">p2</font>,<font color="Maroon" title="c12">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:73"><span class="lab"><font color="Green" title="E71">A22</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
;<br/>
<span class="lab"><font color="Green" title="E80">A32</font></span>: <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D8" target="_self" title="TURING_1:def.8">Def8</a></span>
<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="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p3">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D8" target="_self" title="TURING_1:def.8">Def8</a></span>
<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="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D8" target="_self" title="TURING_1:def.8">Def8</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">4,<font color="Maroon" title="c4">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:73"><span class="lab"><font color="Green" title="E78">A30</font></span></a>, <a class="txt" href="#E50:73"><span class="lab"><font color="Green" title="E79">A31</font></span></a>, <a class="txt" href="#E43:73"><span class="lab"><font color="Green" title="E75">A27</font></span></a>, <a class="txt" href="#E46:73"><span class="lab"><font color="Green" title="E77">A29</font></span></a>, <a class="ref" href="turing_1.html#T12" target="_self" title="TURING_1:th.12">Th12</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E81">A33</font></span>: <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="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  = 
4
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>
<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> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D20" target="_self" title="TURING_1:def.20">Def20</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E53:73"/>
<font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D9" target="_self" title="TURING_1:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font> &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<a NAME="E54:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A34</font></span>: 
 <a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c2">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:73"><span class="lab"><font color="Green" title="E81">A33</font></span></a>, <a class="ref" href="turing_1.html#D10" target="_self" title="TURING_1:def.10">Def10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E55:73"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:73"><span class="lab"><font color="Green" title="E80">A32</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<a NAME="E56:73"/><span class="lab"><font color="Green" title="E83">A35</font></span>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:73"><span class="lab"><font color="Green" title="E80">A32</font></span></a>, <a class="txt" href="#E54:73"><span class="lab"><font color="Green" title="E82">A34</font></span></a>, <a class="ref" href="mcart_1.html#T68" title="MCART_1:th.68">MCART_1:68</a></span>;<br/>
<a NAME="E57:73"/>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<a NAME="E58:73"/><span class="kw">then </span>
<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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:73"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="turing_1.html#T30" target="_self" title="TURING_1:th.30">Th30</a></span>;<br/>
<a NAME="E59:73"/><span class="kw">then </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="c3">t</font>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font></span>)</span>,<font color="Maroon" title="c12">i2</font>,<font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c7">h1</font>,<font color="Maroon" title="c13">T</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c4">h</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:73"><span class="lab"><font color="Green" title="E59">A10</font></span></a>, <a class="txt" href="#E24:73"><span class="lab"><font color="Green" title="E64">A15</font></span></a>, <a class="ref" href="turing_1.html#D13" target="_self" title="TURING_1:def.13">Def13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E60:73"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K11" title="TURING_1:func.11">Result</a> <font color="Maroon" title="c2">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="c4">h</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:73"><span class="lab"><font color="Green" title="E83">A35</font></span></a>, <a class="ref" href="turing_1.html#T19" target="_self" title="TURING_1:th.19">Th19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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