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<span class="kw">reconsider </span><font color="Maroon" title="c1">F</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  as   <a href="turing_1.html#NM3" title="TURING_1:NM.3">Symbol</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E69"><span class="lab"><font color="Green" title="E49">Lm12</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#K19" title="TURING_1:func.19">U3(n)Turing</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a><br/>  for <font color="Olive" title="b2">head</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <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> 3 &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#K5" title="NUMBERS:func.5">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#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">head</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">head</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></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#K19" title="TURING_1:func.19">U3(n)Turing</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">head</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <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> 3 &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#K5" title="NUMBERS:func.5">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#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">head</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">head</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st  <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> 3 &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#K5" title="NUMBERS:func.5">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#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></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#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <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> 3 &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#K5" title="NUMBERS:func.5">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#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></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="E2:76"/><span class="lab"><font color="Green" title="E53">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> 3
 <span class="kw">and </span><br/><a NAME="E3:76"/><span class="lab"><font color="Green" title="E54">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#K5" title="NUMBERS:func.5">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="E4:76"/><span class="lab"><font color="Green" title="E55">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="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#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">n1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">n2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">n3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<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#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">s03</font> = <font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> ;<br/>
<a NAME="E6:76"/><span class="lab"><font color="Green" title="E56">A4</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#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:76"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="turing_1.html#T23" target="_self" onmouseover="rs('turing_1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E7:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A5</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#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="lab"><font color="Green" title="E58">A6</font></span>:  <a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c2">s</font> = 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">s03</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">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#D21" target="_self" onmouseover="rs('turing_1/D21')" onmouseout="rh()">Def21</a></span>
<br/>.= 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">s03</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">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="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>
<br/>.= 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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#K5" title="NUMBERS:func.5">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#K6" title="TURING_1:func.6">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="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></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#K5" title="NUMBERS:func.5">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="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E7:76"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="turing_1.html#T36" target="_self" onmouseover="rs('turing_1/T36')" onmouseout="rh()">Th36</a></span>
;<br/>
<a NAME="E9:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A7</font></span>: 
 <a href="turing_1.html#K5" title="TURING_1:func.5">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
;<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#K19" title="TURING_1:func.19">U3(n)Turing</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E68"><span class="lab"><font color="Green" title="E48">Lm11</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">m1</font> = <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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">h1</font> = <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" onmouseover="rs('int_1/D2')" onmouseout="rh()">INT_1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">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="c12">h1</font>,<font color="Maroon" title="c3">t</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
<a NAME="E12:76"/><span class="lab"><font color="Green" title="E60">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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:76"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="turing_1.html#T23" target="_self" onmouseover="rs('turing_1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E13:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A9</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<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#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">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#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>) = 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c3">t</font>,<span class="p1">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">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#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>
<br/>.= 
 <a href="turing_1.html#K4" title="TURING_1:func.4">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#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>
<br/>.= 
 <a href="turing_1.html#K4" title="TURING_1:func.4">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="#E8:76"><span class="lab"><font color="Green" title="E58">A6</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c3">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:76"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="turing_1.html#T24" target="_self" onmouseover="rs('turing_1/T24')" onmouseout="rh()">Th24</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E62">A10</font></span>:  <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <font color="Maroon" title="c2">s</font> = 
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">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="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="turing_1.html#E70"><span class="lab"><font color="Green" title="E50">Lm13</font></span></a></span>
<br/>.= 
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default">1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">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="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:76"><span class="lab"><font color="Green" title="E58">A6</font></span></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="c12">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="#E3:76"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E9:76"><span class="lab"><font color="Green" title="E59">A7</font></span></a></span>
;<br/>
<a NAME="E16:76"/><span class="lab"><font color="Green" title="E63">A11</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<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#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:76"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="turing_1.html#T23" target="_self" onmouseover="rs('turing_1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E17:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A12</font></span>: 
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 6</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">p2</font> = 2 as   <a href="turing_1.html#NM1" title="TURING_1:NM.1">State</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="turing_1.html#E68"><span class="lab"><font color="Green" title="E48">Lm11</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">s2</font> = <span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">s23</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">j1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">k1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" onmouseover="rs('int_1/D2')" onmouseout="rh()">INT_1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">m2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">Rs</font> = <span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">m3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/>
<div><span class="lab"><font color="Green" title="E65">A13</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="76_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c22">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c22">i</font> &amp; <font color="Maroon" title="c22">i</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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> implies <font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:76_4"/><span class="lab"><font color="Green" title="E66">A14</font></span>: 
<font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c22">i</font>
 <span class="kw">and </span><br/><a NAME="E2:76_4"/><span class="lab"><font color="Green" title="E67">A15</font></span>: 
<font color="Maroon" title="c22">i</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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E3:76_4"/>
<font color="Maroon" title="c4">h</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#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/><a NAME="E4:76_4"/><span class="kw">then </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="c22">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_4"><span class="lab"><font color="Green" title="E66">A14</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:76_4"/>
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:76"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E2:76_4"><span class="lab"><font color="Green" title="E67">A15</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E22:76"/>
(  the <a href="turing_1.html#U3" title="TURING_1:sel.3">Tran</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</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"><font color="Maroon" title="c10">p1</font>,1</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"><font color="Maroon" title="c10">p1</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c10">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D21" target="_self" onmouseover="rs('turing_1/D21')" onmouseout="rh()">Def21</a>, <a class="ref" href="turing_1.html#T36" target="_self" onmouseover="rs('turing_1/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">t1</font> being   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a><span class="kw"> such that </span><br/><a NAME="E24:76"/><span class="lab"><font color="Green" title="E66">A16</font></span>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E25:76"/>
 for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">and </span><br/><a NAME="E26:76"/><span class="lab"><font color="Green" title="E67">A17</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st ( <font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Olive" title="b1">i</font> or <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> ) holds <br/><font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:76"><span class="lab"><font color="Green" title="E65">A13</font></span></a>, <a class="txt" href="turing_1.html#E69"><span class="lab"><font color="Green" title="E49">Lm12</font></span></a>, <a class="txt" href="turing_1.html#E71"><span class="lab"><font color="Green" title="E51">Lm14</font></span></a></span>;<br/>
<a NAME="E27:76"/>
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:76"><span class="lab"><font color="Green" title="E56">A4</font></span></a></span>;<br/>
<a NAME="E28:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A18</font></span>: 
<font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:76"><span class="lab"><font color="Green" title="E67">A17</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E69">A19</font></span>:  <a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c16">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#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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#D21" target="_self" onmouseover="rs('turing_1/D21')" onmouseout="rh()">Def21</a></span>
<br/>.= 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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="c16">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#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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="txt" href="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a></span>
<br/>.= 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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">1,<span class="p2">(<span class="default"><font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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="txt" href="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">2,<a href="numbers.html#K5" title="NUMBERS:func.5">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="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a>, <a class="txt" href="#E28:76"><span class="lab"><font color="Green" title="E68">A18</font></span></a>, <a class="ref" href="turing_1.html#T36" target="_self" onmouseover="rs('turing_1/T36')" onmouseout="rh()">Th36</a></span>
;<br/>
<a NAME="E30:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A20</font></span>: 
 <a href="turing_1.html#K5" title="TURING_1:func.5">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">s3</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>;<br/>
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>) = 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c22">t1</font>,<span class="p1">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a></span>
<br/>.= 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c22">t1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a></span>
<br/>.= 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c22">t1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c1">F</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:76"><span class="lab"><font color="Green" title="E69">A19</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c22">t1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:76"><span class="lab"><font color="Green" title="E68">A18</font></span></a>, <a class="ref" href="turing_1.html#T24" target="_self" onmouseover="rs('turing_1/T24')" onmouseout="rh()">Th24</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E71">A21</font></span>:  <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p0">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">t1</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a>, <a class="txt" href="turing_1.html#E70"><span class="lab"><font color="Green" title="E50">Lm13</font></span></a></span>
<br/>.= 
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default">2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p0">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c22">t1</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:76"><span class="lab"><font color="Green" title="E69">A19</font></span></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="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</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="#E24:76"><span class="lab"><font color="Green" title="E66">A16</font></span></a>, <a class="txt" href="#E30:76"><span class="lab"><font color="Green" title="E70">A20</font></span></a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E72">A22</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="76_8"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">i</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">i</font> &amp; <font color="Maroon" title="c24">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> implies <font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:76_8"/><span class="lab"><font color="Green" title="E73">A23</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">i</font>
 <span class="kw">and </span><br/><a NAME="E2:76_8"/><span class="lab"><font color="Green" title="E74">A24</font></span>: 
<font color="Maroon" title="c24">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E3:76_8"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/><a NAME="E4:76_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A25</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_8"><span class="lab"><font color="Green" title="E73">A23</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">i</font> = 
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:76"><span class="lab"><font color="Green" title="E67">A17</font></span></a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:76"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E2:76_8"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E4:76_8"><span class="lab"><font color="Green" title="E75">A25</font></span></a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c24">s4</font> = <span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c25">s43</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  as   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> ;<br/>
<a NAME="E35:76"/>
(  the <a href="turing_1.html#U3" title="TURING_1:sel.3">Tran</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</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"><font color="Maroon" title="c14">p2</font>,1</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"><font color="Maroon" title="c14">p2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c14">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D21" target="_self" onmouseover="rs('turing_1/D21')" onmouseout="rh()">Def21</a>, <a class="ref" href="turing_1.html#T36" target="_self" onmouseover="rs('turing_1/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">t2</font> being   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a><span class="kw"> such that </span><br/><a NAME="E37:76"/><span class="lab"><font color="Green" title="E73">A26</font></span>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c26">t2</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E38:76"/>
 for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/><font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">and </span><br/><a NAME="E39:76"/><span class="lab"><font color="Green" title="E74">A27</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Olive" title="b1">i</font> or <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> ) holds <br/><font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:76"><span class="lab"><font color="Green" title="E72">A22</font></span></a>, <a class="txt" href="turing_1.html#E69"><span class="lab"><font color="Green" title="E49">Lm12</font></span></a>, <a class="txt" href="turing_1.html#E71"><span class="lab"><font color="Green" title="E51">Lm14</font></span></a></span>;<br/>
<a NAME="E40:76"/>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" onmouseover="rs('nat_1/T12')" onmouseout="rh()">NAT_1:12</a></span>;<br/>
<a NAME="E41:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A28</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T7" onmouseover="rs('xreal_1/T7')" onmouseout="rh()">XREAL_1:7</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E76">A29</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="76_9"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 holds <br/><font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c27">k</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c27">k</font> &amp; <font color="Maroon" title="c27">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 implies <font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:76_9"/><span class="lab"><font color="Green" title="E77">A30</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c27">k</font>
 <span class="kw">and </span><br/><a NAME="E2:76_9"/><span class="lab"><font color="Green" title="E78">A31</font></span>: 
<font color="Maroon" title="c27">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E3:76_9"/><span class="lab"><font color="Green" title="E79">A32</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c27">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:76"><span class="lab"><font color="Green" title="E75">A28</font></span></a>, <a class="txt" href="#E1:76_9"><span class="lab"><font color="Green" title="E77">A30</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">k</font> = 
<font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:76"><span class="lab"><font color="Green" title="E74">A27</font></span></a>, <a class="txt" href="#E1:76_9"><span class="lab"><font color="Green" title="E77">A30</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c3">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:76"><span class="lab"><font color="Green" title="E67">A17</font></span></a>, <a class="txt" href="#E3:76_9"><span class="lab"><font color="Green" title="E79">A32</font></span></a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:76"><span class="lab"><font color="Green" title="E63">A11</font></span></a>, <a class="txt" href="#E1:76_9"><span class="lab"><font color="Green" title="E77">A30</font></span></a>, <a class="txt" href="#E2:76_9"><span class="lab"><font color="Green" title="E78">A31</font></span></a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="lab"><font color="Green" title="E77">A33</font></span>: <font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:76"><span class="lab"><font color="Green" title="E74">A27</font></span></a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:76"><span class="lab"><font color="Green" title="E61">A9</font></span></a>, <a class="txt" href="#E26:76"><span class="lab"><font color="Green" title="E67">A17</font></span></a>, <a class="txt" href="#E41:76"><span class="lab"><font color="Green" title="E75">A28</font></span></a></span>
;<br/>
<span class="lab"><font color="Green" title="E78">A34</font></span>:  <a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c25">s43</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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#D21" target="_self" onmouseover="rs('turing_1/D21')" onmouseout="rh()">Def21</a></span>
<br/>.= 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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="c14">p2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c25">s43</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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="txt" href="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></a></span>
<br/>.= 
<a href="turing_1.html#K18" title="TURING_1:func.18">U3(n)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">2,<span class="p2">(<span class="default"><font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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="txt" href="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></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#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></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="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></a>, <a class="txt" href="#E43:76"><span class="lab"><font color="Green" title="E77">A33</font></span></a>, <a class="ref" href="turing_1.html#T36" target="_self" onmouseover="rs('turing_1/T36')" onmouseout="rh()">Th36</a></span>
;<br/>
<a NAME="E45:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A35</font></span>: 
 <a href="turing_1.html#K5" title="TURING_1:func.5">offset</a> <span class="p1">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a></span>)</span>,<span class="p1">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>) = 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c26">t2</font>,<span class="p1">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></a></span>
<br/>.= 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c26">t2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></a></span>
<br/>.= 
 <a href="turing_1.html#K4" title="TURING_1:func.4">Tape-Chg</a> (<font color="Maroon" title="c26">t2</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c1">F</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:76"><span class="lab"><font color="Green" title="E78">A34</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c26">t2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:76"><span class="lab"><font color="Green" title="E77">A33</font></span></a>, <a class="ref" href="turing_1.html#T24" target="_self" onmouseover="rs('turing_1/T24')" onmouseout="rh()">Th24</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E80">A36</font></span>:  <a href="turing_1.html#K8" title="TURING_1:func.8">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c26">t2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></a>, <a class="txt" href="turing_1.html#E70"><span class="lab"><font color="Green" title="E50">Lm13</font></span></a></span>
<br/>.= 
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default">3,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K6" title="TURING_1:func.6">Head</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</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#K5" title="TURING_1:func.5">offset</a> <span class="p4">(<span class="default"><a href="turing_1.html#K7" title="TURING_1:func.7">TRAN</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c26">t2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:76"><span class="lab"><font color="Green" title="E78">A34</font></span></a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">3,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p0">(<span class="default"><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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<font color="Maroon" title="c26">t2</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="#E37:76"><span class="lab"><font color="Green" title="E73">A26</font></span></a>, <a class="txt" href="#E45:76"><span class="lab"><font color="Green" title="E79">A35</font></span></a></span>
;<br/>
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T10" target="_self" onmouseover="rs('turing_1/T10')" onmouseout="rh()">Th10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:76"><span class="lab"><font color="Green" title="E62">A10</font></span></a>, <a class="ref" href="turing_1.html#T9" target="_self" onmouseover="rs('turing_1/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T10" target="_self" onmouseover="rs('turing_1/T10')" onmouseout="rh()">Th10</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E81">A37</font></span>: <span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p0"><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="c12">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="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#T10" target="_self" onmouseover="rs('turing_1/T10')" onmouseout="rh()">Th10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c14">p2</font>,<font color="Maroon" title="c18">k1</font>,<font color="Maroon" title="c22">t1</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:76"><span class="lab"><font color="Green" title="E71">A21</font></span></a>, <a class="ref" href="turing_1.html#T9" target="_self" onmouseover="rs('turing_1/T9')" onmouseout="rh()">Th9</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">3,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c26">t2</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="#E47:76"><span class="lab"><font color="Green" title="E80">A36</font></span></a>, <a class="ref" href="turing_1.html#D7" target="_self" onmouseover="rs('turing_1/D7')" onmouseout="rh()">Def7</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E82">A38</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K9" title="TURING_1:func.9">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a>  = 
3

<br/>.= 
 the <a href="turing_1.html#U5" title="TURING_1:sel.5">AcceptS</a> of <a href="turing_1.html#K19" title="TURING_1:func.19">U3(n)Turing</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="turing_1.html#D21" target="_self" onmouseover="rs('turing_1/D21')" onmouseout="rh()">Def21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E51:76"/>
<font color="Maroon" title="c2">s</font> is  <a href="turing_1.html#V2" title="TURING_1:attr.2">Accept-Halt</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>

<a NAME="E52:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A39</font></span>: 
 <a href="turing_1.html#K10" title="TURING_1:func.10">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#K9" title="TURING_1:func.9">Computation</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:76"><span class="lab"><font color="Green" title="E82">A38</font></span></a>, <a class="ref" href="turing_1.html#D9" target="_self" onmouseover="rs('turing_1/D9')" onmouseout="rh()">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E53:76"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:76"><span class="lab"><font color="Green" title="E81">A37</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<a NAME="E54:76"/><span class="lab"><font color="Green" title="E84">A40</font></span>: 
<span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">t2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:76"><span class="lab"><font color="Green" title="E81">A37</font></span></a>, <a class="txt" href="#E52:76"><span class="lab"><font color="Green" title="E83">A39</font></span></a></span>;<br/>
<a NAME="E55:76"/><span class="lab"><font color="Green" title="E85">A41</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<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#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" onmouseover="rs('nat_1/T11')" onmouseout="rh()">NAT_1:11</a></span>;<br/>
<a NAME="E56:76"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A42</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:76"><span class="lab"><font color="Green" title="E75">A28</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<font color="Maroon" title="c26">t2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p0">(<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#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> = 
<font color="Maroon" title="c22">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p0">(<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#K1" title="NAT_1:func.1">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:76"><span class="lab"><font color="Green" title="E74">A27</font></span></a>, <a class="txt" href="#E55:76"><span class="lab"><font color="Green" title="E85">A41</font></span></a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:76"><span class="lab"><font color="Green" title="E64">A12</font></span></a>, <a class="txt" href="#E26:76"><span class="lab"><font color="Green" title="E67">A17</font></span></a>, <a class="txt" href="#E56:76"><span class="lab"><font color="Green" title="E86">A42</font></span></a></span>
;<br/>
<a NAME="E58:76"/><span class="kw">then </span>
<font color="Maroon" title="c26">t2</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<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#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:76"><span class="lab"><font color="Green" title="E77">A33</font></span></a>, <a class="txt" href="#E42:76"><span class="lab"><font color="Green" title="E76">A29</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E59:76"/>
<span class="p1">(<span class="default"><a href="turing_1.html#K10" title="TURING_1:func.10">Result</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p5">(<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#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span></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="#E54:76"><span class="lab"><font color="Green" title="E84">A40</font></span></a>, <a class="ref" href="turing_1.html#T16" target="_self" onmouseover="rs('turing_1/T16')" onmouseout="rh()">Th16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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