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

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> <a href="ami_1.html#V10" title="AMI_1:attr.10">realistic</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">loc</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:105"/><i><font color="Green" title="E59">A1</font></i>: 
<font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">loc</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">h</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c3">loc</font>;<br/>

<b>assume </b><a NAME="E2:105"/><i><font color="Green" title="E60">A2</font></i>: 
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 ;<br/>

<b>thus </b><a NAME="E3:105"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">autonomic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25" target="_self" title="AMI_1:def.25">AMI_1:def 25</a><br/>

<b>assume </b><a NAME="E1:105_1"/><i><font color="Green" title="E61">A3</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s1</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font> )
 ;<br/>

<a NAME="E2:105_1"/><b>then </b><i><font color="Green" title="E62">A4</font></i>: 
( <font color="Maroon" title="c6">s1</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font> &amp; <font color="Maroon" title="c7">s2</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font> )
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T64" title="GRFUNC_1:th.64">GRFUNC_1:64</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<a NAME="E3:105_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c6">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s1</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c7">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s2</font> )
 
<b>by </b><i><a class="txt" href="ami_1.html#E1:105"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="ami_1.html#E2:105"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="ami_1.html#E1:105_1"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="ami_1.html#T66" target="_self" title="AMI_1:th.66">Th66</a></i>;<br/>
<b>hence </b><a NAME="E4:105_1"/>
<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="c6">s1</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c7">s2</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>,<font color="Maroon" title="c3">loc</font> <a href="ami_1.html#K16" title="AMI_1:func.16">--&gt;</a> <font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:105_1"><i><font color="Green" title="E62">A4</font></i></a></i>;<br/>


</div><b>end;</b></div>


</div>
