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

<b>let </b><font color="Maroon" title="c1">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_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>, <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/>

<a NAME="E1:29"/><i><font color="Green" title="E26">A1</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 0
 
<b>by </b><i><a class="ref" href="scm_1.html#D1" target="_self" title="SCM_1:def.1">Def1</a></i>;<br/>
<a NAME="E2:29"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<b>then </b><i><font color="Green" title="E27">A2</font></i>: <font color="Maroon" title="c1">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#K16" title="AMI_3:func.16">il.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0</span>)</span></span>)</span> = 
<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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="ref" href="scm_1.html#D1" target="_self" title="SCM_1:def.1">Def1</a></i>
<br/>.= 
 <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> 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c2">s0</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0;<br/>
<a NAME="E4:29"/><i><font color="Green" title="E28">A3</font></i>: 
<font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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="E5:29"/><b>then </b>
<font color="Maroon" title="c1">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</span>)</span></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> 
 
<b>by </b><i><a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="scm_1.html#D1" target="_self" title="SCM_1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E6:29"/><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c1">s</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 <b>by </b><i><a class="ref" href="scm_1.html#T3" target="_self" title="SCM_1:th.3">Th3</a></i>;<br/>

<a NAME="E7:29"/>
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> 0</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; ( for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Olive" title="b1">k</font></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>  holds <br/>0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> ) )
 
<b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="scm_1.html#E4:29"><i><font color="Green" title="E28">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:29"/>
 <a href="scm_1.html#K2" title="SCM_1:func.2">Complexity</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="scm_1.html#E6:29"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="scm_1.html#D2" target="_self" title="SCM_1:def.2">Def2</a></i>;<br/>

<b>thus </b><a NAME="E9:29"/>
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font>
 <b>by </b><i><a class="txt" href="scm_1.html#E1:29"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="scm_1.html#E3:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="scm_1.html#E4:29"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="scm_1.html#T4" target="_self" title="SCM_1:th.4">Th4</a></i>;<br/>


</div>
