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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="turing_1.html#L1" title="TURING_1:struct.1">TuringStr</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 <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">n</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>   st <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_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/><font color="Olive" title="b1">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span><br/><span class="kw">let </span><font color="Maroon" title="c2">t</font> be   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <font color="Maroon" title="c1">T</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">  for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">n</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>   st <font color="Maroon" title="c2">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> holds <br/><font color="Maroon" title="c2">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">n</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"> ( <font color="Maroon" title="c2">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> implies <font color="Maroon" title="c2">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c5">f</font> = <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>;<br/>
<span class="kw">assume </span><a NAME="E1:33"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c2">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</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"> <font color="Maroon" title="c2">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span><br/>

<a NAME="E2:33"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>;<br/>
<a NAME="E3:33"/>
( <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p2">(<span class="default"><a href="turing_1.html#NK5" title="TURING_1:NK.5">Prefix</a> (<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,1)</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> &amp; <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p2">(<span class="default"><a href="turing_1.html#NK5" title="TURING_1:NK.5">Prefix</a> (<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">n</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<span class="p3">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font></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="ref" href="turing_1.html#T4" target="_self" onmouseover="rs('turing_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:33"/>
<font color="Maroon" title="c2">t</font> <a href="turing_1.html#R1" title="TURING_1:pred.1">is_1_between</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font></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="#E1:33"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E17">A2</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/>


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