<?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="E1:71"/><i><font color="Green" title="E55">A1</font></i>: 
not <font color="Maroon" title="c2">R</font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">p</font> be  <a href="ami_1.html#V11" title="AMI_1:attr.11">autonomic</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c2">R</font>;<br/>

<b>assume </b><a NAME="E2:71"/><i><font color="Green" title="E56">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="E1:71_1"/><i><font color="Green" title="E57">A3</font></i>: 
<font color="Maroon" title="c3">p</font> is <a href="ami_1.html#V12" title="AMI_1:attr.12">halting</a>
 ;<br/><b>thus </b><a NAME="E2:71_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#V12" title="AMI_1:attr.12">halting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_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="E1:71_1_1"/><i><font color="Green" title="E58">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_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c3">p</font>;<br/>
<a NAME="E2:71_1_1"/><i><font color="Green" title="E59">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_5.html#K8" title="AMI_5:func.8">+*</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="E3:71_1_1"/><b>then </b>
<font color="Maroon" title="c4">t</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c3">p</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:71_1"><i><font color="Green" title="E57">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="E5:71_1_1"/><i><font color="Green" title="E60">A6</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">t</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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_5.html#K8" title="AMI_5:func.8">+*</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#K4" title="AMI_2:func.4">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_5.html#T82" title="AMI_5:th.82">AMI_5:82</a></i>;<br/>
<a NAME="E7:71_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="E61">A7</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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="c4">t</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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#E1:71"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="scmring4.html#E2:71"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="scmring4.html#E1:71_1_1"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="scmring4.html#E2:71_1_1"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="scmring4.html#E5:71_1_1"><i><font color="Green" title="E60">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="E9:71_1_1"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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="c4">t</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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#E8:71_1_1"><i><font color="Green" title="E61">A7</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E4:71"/><i><font color="Green" title="E57">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#V12" title="AMI_1:attr.12">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="E5:71"/><i><font color="Green" title="E58">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_5.html#K8" title="AMI_5:func.8">+*</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="E7:71"/><i><font color="Green" title="E59">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_5.html#K8" title="AMI_5:func.8">+*</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="E8:71"/><b>then </b>
<font color="Maroon" title="c5">s</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E4:71"><i><font color="Green" title="E57">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="E10:71"/><i><font color="Green" title="E60">A11</font></i>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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="c5">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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#K4" title="AMI_2:func.4">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_5.html#T82" title="AMI_5:th.82">AMI_5:82</a></i>;<br/>
<a NAME="E12:71"/>
<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="E13:71"/><b>then </b><i><font color="Green" title="E61">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#K8" title="AMI_1:func.8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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#E1:71"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="scmring4.html#E2:71"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="scmring4.html#E5:71"><i><font color="Green" title="E58">A9</font></i></a>, <a class="txt" href="scmring4.html#E7:71"><i><font color="Green" title="E59">A10</font></i></a>, <a class="txt" href="scmring4.html#E10:71"><i><font color="Green" title="E60">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="E14:71"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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="c4">t</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</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#E13:71"><i><font color="Green" title="E61">A12</font></i></a>, <a class="ref" href="amistd_2.html#T35" title="AMISTD_2:th.35">AMISTD_2:35</a></i>;<br/>


</div>
