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<b>let </b><font color="Maroon">T</font> be    <a href="turing_1.html#L1" target="_self">TuringStr</a> ;<br/><b>let </b><font color="Maroon">t</font> be   <a href="turing_1.html#NM2">Tape</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">s</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>set </b><font color="Maroon">f</font> = <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span>;<br/>
<b>assume </b><a NAME="E1:38"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">t</font> <a href="turing_1.html#R2" target="_self">storeData</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 ;<br/>

<a NAME="E2:38"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="gr_cy_1.html#K2">Sum</a> <span class="p2">(<span class="default"><a href="turing_1.html#K4" target="_self">Prefix</a> <span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:38"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="gr_cy_1.html#K2">Sum</a> <span class="p2">(<span class="default"><a href="turing_1.html#K4" target="_self">Prefix</a> <span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span>,<span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i/>;<br/>
<a NAME="E4:38"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><a href="gr_cy_1.html#K2">Sum</a> <span class="p2">(<span class="default"><a href="turing_1.html#K4" target="_self">Prefix</a> <span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span>,2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i/>;<br/>
<a NAME="E5:38"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><a href="gr_cy_1.html#K2">Sum</a> <span class="p2">(<span class="default"><a href="turing_1.html#K4" target="_self">Prefix</a> <span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span> <a href="nat_1.html#K1">+</a> 4
 
<b>by </b><i/>;<br/>
<a NAME="E6:38"/><i><font color="Green">E75</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">n1</font>,<font color="Maroon">n2</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>
<b>hence </b><a NAME="E7:38"/>
<font color="Maroon">t</font> <a href="turing_1.html#R1" target="_self">is_1_between</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i>, , , </i>;<br/>

<b>thus </b><a NAME="E8:38"/>
<font color="Maroon">t</font> <a href="turing_1.html#R1" target="_self">is_1_between</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font></span>)</span> <a href="nat_1.html#K1">+</a> 2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i>, , , <a class="txt" href="turing_1.html#E1:38"><i><font color="Green">E30</font></i></a>, </i>;<br/>


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