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

<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> holds <br/>( <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> iff  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> )</span><br/><b>let </b><font color="Maroon" title="c2">k</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> implies ( <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> iff  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> ) )</span><br/>



<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> iff  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> implies <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:14_1"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><br/><b>thus </b><a NAME="E2:14_1"/>
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">t</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">t</font> or <font color="Maroon" title="c3">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> )</span><br/>

<b>assume </b><a NAME="E1:14_1_1"/><i><font color="Green" title="E16">A3</font></i>: 
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Maroon" title="c1">p</font> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<br/>
<a NAME="E3:14_1_1"/><i><font color="Green" title="E17">A4</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E4:14_1_1"/><b>then </b>
<font color="Maroon" title="c4">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E1:14_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">u</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> <b> such that </b><br/><a NAME="E6:14_1_1"/><i><font color="Green" title="E18">A5</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">u</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">s3</font> = <font color="Maroon" title="c4">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c3">t</font></span>)</span> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<br/>
<i><font color="Green" title="E19">A6</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</font></span>)</span> = 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="scmfsa_5.html#E1:14"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="scmfsa_5.html#E1:14_1_1"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="scmfsa_5.html#E3:14_1_1"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="scmfsa_5.html#E6:14_1_1"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="scmfsa_5.html#T12" target="_self" title="SCMFSA_5:th.12">Th12</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T8" title="SCMFSA_4:th.8">SCMFSA_4:8</a></i>
;<br/>
<b>take </b>
<font color="Maroon" title="c5">u</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span><br/>

<b>thus </b><a NAME="E9:14_1_1"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E8:14_1_1"><i><font color="Green" title="E19">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E3:14"/><i><font color="Green" title="E15">A7</font></i>: 
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a></span><br/>

<b>let </b><font color="Maroon" title="c3">t</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">t</font> or <font color="Maroon" title="c3">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a> )</span><br/>

<b>assume </b><a NAME="E4:14"/><i><font color="Green" title="E16">A8</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">t</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<br/>
<a NAME="E6:14"/><i><font color="Green" title="E17">A9</font></i>: 
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:14"/><b>then </b>
<font color="Maroon" title="c4">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E3:14"><i><font color="Green" title="E15">A7</font></i></a>, <a class="ref" href="ami_1.html#D26" title="AMI_1:def.26">AMI_1:def 26</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">u</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> <b> such that </b><br/><a NAME="E9:14"/><i><font color="Green" title="E18">A10</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">u</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">s3</font> = <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c4">s</font></span>)</span> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<br/>
<a NAME="E11:14"/><i><font color="Green" title="E19">A11</font></i>: 
 <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">k</font> <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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E1:14"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="scmfsa_5.html#E4:14"><i><font color="Green" title="E16">A8</font></i></a>, <a class="txt" href="scmfsa_5.html#E6:14"><i><font color="Green" title="E17">A9</font></i></a>, <a class="txt" href="scmfsa_5.html#E9:14"><i><font color="Green" title="E18">A10</font></i></a>, <a class="ref" href="scmfsa_5.html#T12" target="_self" title="SCMFSA_5:th.12">Th12</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">u</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span><br/>

<a NAME="E12:14"/><i><font color="Green" title="E20">A12</font></i>: 
not  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E13:14"/>
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E11:14"><i><font color="Green" title="E19">A11</font></i></a>, <a class="ref" href="scmfsa_2.html#T124" title="SCMFSA_2:th.124">SCMFSA_2:124</a>, <a class="ref" href="scmfsa_4.html#T22" title="SCMFSA_4:th.22">SCMFSA_4:22</a></i>;<br/>
<b>hence </b><a NAME="E14:14"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c5">u</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E11:14"><i><font color="Green" title="E19">A11</font></i></a>, <a class="txt" href="scmfsa_5.html#E12:14"><i><font color="Green" title="E20">A12</font></i></a>, <a class="ref" href="scmfsa_4.html#D3" title="SCMFSA_4:def.3">SCMFSA_4:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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