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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ami_1.html#V11">autonomic</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E37</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="ami_1.html#V12">halting</a>
 ;<br/><b>thus </b><a NAME="E2:39_1"/>
 <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="ami_1.html#V12">halting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D26">AMI_1:def 26</a><br/>

<b>assume </b><a NAME="E1:39_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  ;<br/>
<a NAME="E3:39_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E4:39_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="reloc.html#E1:39_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:39_1_1"/><i><font color="Green">E41</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> as   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  <b>by </b><i><a class="ref" href="ami_5.html#T82">AMI_5:82</a></i>;<br/>
<a NAME="E8:39_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
;<br/>
<b>then </b><i><font color="Green">E42</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="reloc.html#K3" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="reloc.html#E1:39"><i><font color="Green">E37</font></i></a>, <a class="txt" href="reloc.html#E1:39_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="reloc.html#E3:39_1_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="reloc.html#E6:39_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="reloc.html#T34" target="_self">Th34</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
<b>by </b><i><a class="ref" href="reloc.html#D3" target="_self">Def3</a>, <a class="ref" href="ami_5.html#T37">AMI_5:37</a></i>
;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a><br/>

<b>thus </b><a NAME="E10:39_1_1"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="txt" href="reloc.html#E9:39_1_1"><i><font color="Green">E42</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E3:39"/><i><font color="Green">E38</font></i>: 
 <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="ami_1.html#V12">halting</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D26">AMI_1:def 26</a><br/>

<b>assume </b><a NAME="E4:39"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  ;<br/>
<a NAME="E6:39"/><i><font color="Green">E40</font></i>: 
 <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:39"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="reloc.html#E3:39"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E9:39"/><i><font color="Green">E41</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> as   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  <b>by </b><i><a class="ref" href="ami_5.html#T82">AMI_5:82</a></i>;<br/>
<a NAME="E11:39"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
;<br/>
<a NAME="E12:39"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="reloc.html#K3" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i><a class="txt" href="reloc.html#E1:39"><i><font color="Green">E37</font></i></a>, <a class="txt" href="reloc.html#E4:39"><i><font color="Green">E39</font></i></a>, <a class="txt" href="reloc.html#E6:39"><i><font color="Green">E40</font></i></a>, <a class="txt" href="reloc.html#E9:39"><i><font color="Green">E41</font></i></a>, <a class="ref" href="reloc.html#T34" target="_self">Th34</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a><br/>

<b>thus </b><a NAME="E13:39"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="txt" href="reloc.html#E12:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="reloc.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_5.html#T37">AMI_5:37</a></i>;<br/>


</div>
