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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="turing_1.html#L1" target="_self">TuringStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="turing_1.html#NM2">Tape</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>;<br/>
<b>assume </b><a NAME="E1:38"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 ;<br/>

<a NAME="E2:38"/><i><font color="Green">E26</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="turing_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E3:38"/><i><font color="Green">E27</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="ref" href="turing_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E4:38"/><i><font color="Green">E28</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="ref" href="turing_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E5:38"/><i><font color="Green">E29</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4
 
<b>by </b><i><a class="ref" href="turing_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E6:38"/><i><font color="Green">E30</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font> <a href="turing_1.html#R1" target="_self">is_1_between</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="txt" href="turing_1.html#E1:38"><i><font color="Green">E25</font></i></a>, <a class="txt" href="turing_1.html#E2:38"><i><font color="Green">E26</font></i></a>, <a class="txt" href="turing_1.html#E3:38"><i><font color="Green">E27</font></i></a>, <a class="ref" href="turing_1.html#D14" target="_self">Def14</a></i>;<br/>

<b>thus </b><a NAME="E8:38"/>
<font color="Maroon">c<sub>2</sub></font> <a href="turing_1.html#R1" target="_self">is_1_between</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>5</sub></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">E25</font></i></a>, <a class="txt" href="turing_1.html#E4:38"><i><font color="Green">E28</font></i></a>, <a class="txt" href="turing_1.html#E5:38"><i><font color="Green">E29</font></i></a>, <a class="txt" href="turing_1.html#E6:38"><i><font color="Green">E30</font></i></a>, <a class="ref" href="turing_1.html#D14" target="_self">Def14</a></i>;<br/>


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