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<b>let </b><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">i2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 1</span>)</span></span>)</span></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> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c2">i2</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> holds <br/> ( <font color="Olive" title="b1">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; ( for <font color="Olive" title="b2">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b2">d</font> ) )</span><br/><b>let </b><font color="Maroon" title="c3">s</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 1</span>)</span></span>)</span></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> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c2">i2</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> &amp;  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; ( for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> ) )</span><br/>



<a NAME="E1:31"/><i><font color="Green" title="E21">A1</font></i>: 
(  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K9" title="AMI_3:func.9">=0_goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 1</span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  &amp; <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> &amp; <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i2</font> )
 
<b>by </b><i><a class="ref" href="scm_1.html#T15" target="_self" title="SCM_1:th.15">Th15</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">s1</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<a NAME="E2:31"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a></i>;<br/>
<a NAME="E3:31"/><i><font color="Green" title="E23">A3</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scm_1.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:31"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="scm_1.html#T24" target="_self" title="SCM_1:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E4:31"/>
<font color="Maroon" title="c3">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 <b>by </b><i><a class="txt" href="scm_1.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="scm_1.html#T3" target="_self" title="SCM_1:th.3">Th3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; ( for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> ) )</span><br/>

<b>thus </b><a NAME="E5:31"/>
 <a href="ami_1.html#K31" title="AMI_1:func.31">LifeSpan</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="scm_1.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:31"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="scm_1.html#E3:31"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="scm_1.html#T17" target="_self" title="SCM_1:th.17">Th17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font></span><br/>

<b>let </b><font color="Maroon" title="c5">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font></span><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="scm_1.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scm_1.html#E3:31"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="scm_1.html#T4" target="_self" title="SCM_1:th.4">Th4</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="scm_1.html#E1:31"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:31"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="scm_1.html#T24" target="_self" title="SCM_1:th.24">Th24</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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