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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2" target="_self">void</a> <a href="ami_1.html#V4" target="_self">halting</a> <a href="ami_1.html#V5" target="_self">IC-Ins-separated</a> <a href="ami_1.html#V8" target="_self">definite</a> <a href="ami_1.html#V10" target="_self">realistic</a>  <a href="ami_1.html#L1" target="_self">AMI-Struct</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3" target="_self">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:104"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3" target="_self">ObjectKind</a> <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E2:104"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E3:104"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> is <a href="ami_1.html#V11" target="_self">autonomic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25" target="_self">AMI_1:def 25</a><br/>

<b>assume </b><a NAME="E1:104_1"/><i><font color="Green">E61</font></i>: 
( <span class="p1">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<a NAME="E2:104_1"/><b>then </b><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E3:104_1"/>
( <span class="p1">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="ami_1.html#E1:104"><i><font color="Green">E59</font></i></a>, <a class="txt" href="ami_1.html#E2:104"><i><font color="Green">E60</font></i></a>, <a class="txt" href="ami_1.html#E1:104_1"><i><font color="Green">E61</font></i></a>, <a class="ref" href="ami_1.html#T66" target="_self">Th66</a></i>;<br/>
<b>hence </b><a NAME="E4:104_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" target="_self">IC</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_1.html#K16" target="_self">--&gt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:104_1"><i><font color="Green">E62</font></i></a></i>;<br/>


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


</div>
