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

<span class="kw">let </span><font color="Maroon" title="c1">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</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#V7" title="AMI_1:attr.7">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#V9" title="AMI_1:attr.9">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/> for <font color="Olive" title="b2">l</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b3">p</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b3">p</font> <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="Olive" title="b1">S</font></span>)</span>,<font color="Olive" title="b2">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b2">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Olive" title="b1">S</font></span>)</span> holds <br/><font color="Olive" title="b3">p</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</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#V7" title="AMI_1:attr.7">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">l</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">p</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b2">p</font> <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="Olive" title="b1">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b1">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span> holds <br/><font color="Olive" title="b2">p</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">p</font> <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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span> holds <br/><font color="Olive" title="b1">p</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> </span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">h</font> =  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">p</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">p</font> <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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span> implies <font color="Maroon" title="c5">p</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:129"/><span class="lab"><font color="Green" title="E37">Z</font></span>: 
<font color="Maroon" title="c5">p</font> <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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">p</font> is  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D25" target="_self" title="AMI_1:def.25">AMI_1:def 25</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s1</font> &amp; <font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font> implies for <font color="Olive" title="b1">i</font> being   <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>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c6">s1</font>,<font color="Olive" title="b1">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> <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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c7">s2</font>,<font color="Olive" title="b1">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:129"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s1</font>
 <span class="kw">and </span><br/><a NAME="E3:129"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">s2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <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>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c6">s1</font>,<font color="Olive" title="b1">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> <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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c7">s2</font>,<font color="Olive" title="b1">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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span></span><br/>

<a NAME="E4:129"/><span class="lab"><font color="Green" title="E40">A5</font></span>: 
( <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#NK2" title="RELAT_1:NK.2">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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span></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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span> &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#NK2" title="RELAT_1:NK.2">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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span></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">l</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">l</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129"><span class="lab"><font color="Green" title="E37">Z</font></span></a>, <a class="txt" href="#E2:129"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E3:129"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T64" title="GRFUNC_1:th.64">GRFUNC_1:64</a></span>;<br/>
<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c6">s1</font>,<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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> <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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c7">s2</font>,<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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span></span><br/>

<a NAME="E5:129"/>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129"><span class="lab"><font color="Green" title="E37">Z</font></span></a>, <a class="txt" href="#E2:129"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="ami_1.html#T66" target="_self" title="AMI_1:th.66">Th66</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:129"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c6">s1</font>,<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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span> <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">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c7">s2</font>,<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#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129"><span class="lab"><font color="Green" title="E37">Z</font></span></a>, <a class="txt" href="#E3:129"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="txt" href="#E4:129"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="ami_1.html#T66" target="_self" title="AMI_1:th.66">Th66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
