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

<b>let </b><font color="Maroon" title="c1">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be  <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a> <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/>



<b>assume </b><a NAME="E1:69"/><i><font color="Green" title="E54">A1</font></i>: 
not <font color="Maroon" title="c2">R</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">p</font> be  <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:69"/><i><font color="Green" title="E55">A2</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">p</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:69_1"/><i><font color="Green" title="E56">A3</font></i>: 
<font color="Maroon" title="c3">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 ;<br/><b>thus </b><a NAME="E2:69_1"/>
 <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">t</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>; <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><br/>

<b>assume </b><a NAME="E1:69_1_1"/><i><font color="Green" title="E57">A4</font></i>: 
 <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">t</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c3">p</font>;<br/>
<a NAME="E2:69_1_1"/><i><font color="Green" title="E58">A5</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c3">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="E3:69_1_1"/><b>then </b>
<font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c3">p</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:69_1"><i><font color="Green" title="E56">A3</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="c6">u</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> <b> such that </b><br/><a NAME="E5:69_1_1"/><i><font color="Green" title="E59">A6</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <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="c7">s3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#T113" title="AMI_1:th.113">AMI_1:113</a></i>;<br/>
<a NAME="E7:69_1_1"/>
<font color="Maroon" title="c7">s3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s3</font>
 
;<br/>
<b>then </b><i><font color="Green" title="E60">A7</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c6">u</font></span>)</span> = 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="txt" href="scmring4.html#E1:69"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="scmring4.html#E2:69"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="scmring4.html#E1:69_1_1"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="scmring4.html#E2:69_1_1"><i><font color="Green" title="E58">A5</font></i></a>, <a class="txt" href="scmring4.html#E5:69_1_1"><i><font color="Green" title="E59">A6</font></i></a>, <a class="ref" href="scmring4.html#T59" target="_self" title="SCMRING4:th.59">Th59</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T29" title="AMISTD_2:th.29">AMISTD_2:29</a></i>
;<br/>
<b>take </b>
<font color="Maroon" title="c6">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><br/>

<b>thus </b><a NAME="E9:69_1_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E8:69_1_1"><i><font color="Green" title="E60">A7</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E4:69"/><i><font color="Green" title="E56">A8</font></i>: 
 <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">t</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>; <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><br/>

<b>assume </b><a NAME="E5:69"/><i><font color="Green" title="E57">A9</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">t</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font></span>)</span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> ;<br/>
<a NAME="E7:69"/><i><font color="Green" title="E58">A10</font></i>: 
 <a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">t</font> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" title="SCMRING4:func.3">Relocated</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c1">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="E8:69"/><b>then </b>
<font color="Maroon" title="c5">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E4:69"><i><font color="Green" title="E56">A8</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="c6">u</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> <b> such that </b><br/><a NAME="E10:69"/><i><font color="Green" title="E59">A11</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <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="c7">s3</font> = <font color="Maroon" title="c4">t</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#T113" title="AMI_1:th.113">AMI_1:113</a></i>;<br/>
<a NAME="E12:69"/>
<font color="Maroon" title="c7">s3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s3</font>
 
;<br/>
<a NAME="E13:69"/><b>then </b><i><font color="Green" title="E60">A12</font></i>: 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c6">u</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:69"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="scmring4.html#E2:69"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="scmring4.html#E5:69"><i><font color="Green" title="E57">A9</font></i></a>, <a class="txt" href="scmring4.html#E7:69"><i><font color="Green" title="E58">A10</font></i></a>, <a class="txt" href="scmring4.html#E10:69"><i><font color="Green" title="E59">A11</font></i></a>, <a class="ref" href="scmring4.html#T59" target="_self" title="SCMRING4:th.59">Th59</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">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><br/>

<b>thus </b><a NAME="E14:69"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E13:69"><i><font color="Green" title="E60">A12</font></i></a>, <a class="ref" href="amistd_2.html#T35" title="AMISTD_2:th.35">AMISTD_2:35</a></i>;<br/>


</div>
