<?xml version="1.0"?>
<div class="add">

<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>;<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 0,0,0,<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_3.html#K5" title="AMI_3:func.5">SubFrom</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</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>;<br/>



<a NAME="E1:29"/><i><font color="Green" title="E22">A1</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 0 &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K5" title="AMI_3:func.5">SubFrom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> &amp; <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">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#K12" title="AMI_3:func.12">dl.</a> 0</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#K12" title="AMI_3:func.12">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">s0</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 0;<br/>
<b>set </b><font color="Maroon" title="c5">s1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E2:29"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 0
 
<b>by </b><i><a class="ref" href="ami_1.html#D19" title="AMI_1:def.19">AMI_1:def 19</a></i>;<br/>
<a NAME="E3:29"/><b>then </b><i><font color="Green" title="E24">A3</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">0 <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="ami_3.html#K13" title="AMI_3:func.13">il.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="scm_1.html#T20" target="_self" title="SCM_1:th.20">Th20</a></i>;<br/>
<a NAME="E4:29"/><i><font color="Green" title="E25">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 0</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> 0</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:29"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="scm_1.html#T20" target="_self" title="SCM_1:th.20">Th20</a></i>;<br/>
<b>thus </b><a NAME="E5:29"/>
<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#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="scm_1.html#T3" target="_self" title="SCM_1:th.3">Th3</a></i>;<br/>

<a NAME="E6:29"/>
 <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K13" title="AMI_3:func.13">il.</a> 1
 
<b>by </b><i><a class="ref" href="ami_3.html#T53" title="AMI_3:th.53">AMI_3:53</a></i>;<br/>
<b>hence </b><a NAME="E7:29"/>
 <a href="ami_1.html#K29" title="AMI_1:func.29">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#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:29"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="scm_1.html#T17" target="_self" title="SCM_1:th.17">Th17</a></i>;<br/>

<b>thus </b><a NAME="E8:29"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">i2</font>
 <b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:29"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="scm_1.html#E4:29"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="scm_1.html#T4" target="_self" title="SCM_1:th.4">Th4</a></i>;<br/>

<b>let </b><font color="Maroon" title="c6">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>

<b>assume </b><a NAME="E9:29"/><i><font color="Green" title="E26">A5</font></i>: 
<font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 0
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">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="c6">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c6">d</font>
<b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E24">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="c6">d</font>
<b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="scm_1.html#E2:29"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="scm_1.html#E9:29"><i><font color="Green" title="E26">A5</font></i></a>, <a class="ref" href="scm_1.html#T20" target="_self" title="SCM_1:th.20">Th20</a></i>
;<br/>


</div>
