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<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#NM7" title="AMI_1:NM.7">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>let </b><font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:31_1"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a>
 ;<br/><b>thus </b><a NAME="E2:31_1"/>
 <a href="reloc.html#K3" title="RELOC:func.3">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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_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="ami_3.html#K1" title="AMI_3:func.1">SCM</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><br/>

<b>assume </b><a NAME="E1:31_1_1"/><i><font color="Green" title="E32">A3</font></i>: 
 <a href="reloc.html#K3" title="RELOC:func.3">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>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</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="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  ;<br/>
<a NAME="E3:31_1_1"/><i><font color="Green" title="E33">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#K34" title="AMI_1:func.34">+*</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="E4:31_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="reloc.html#E1:31_1"><i><font color="Green" title="E31">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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:31_1_1"/><i><font color="Green" title="E34">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="ami_3.html#K1" title="AMI_3:func.1">SCM</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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">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#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <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="E8:31_1_1"/>
<font color="Maroon" title="c6">s3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s3</font>
 
;<br/>
<b>then </b><i><font color="Green" title="E35">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="reloc.html#K1" title="RELOC: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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="reloc.html#E1:31"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="reloc.html#E1:31_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="reloc.html#E3:31_1_1"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="reloc.html#E6:31_1_1"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="reloc.html#T34" target="_self" title="RELOC:th.34">Th34</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
<b>by </b><i><a class="ref" href="reloc.html#D3" target="_self" title="RELOC:def.3">Def3</a>, <a class="ref" href="ami_5.html#T37" title="AMI_5:th.37">AMI_5:37</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><br/>

<b>thus </b><a NAME="E10:31_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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="txt" href="reloc.html#E9:31_1_1"><i><font color="Green" title="E35">A6</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E3:31"/><i><font color="Green" title="E31">A7</font></i>: 
 <a href="reloc.html#K3" title="RELOC:func.3">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>
 ;<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="ami_3.html#K1" title="AMI_3:func.1">SCM</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><br/>

<b>assume </b><a NAME="E4:31"/><i><font color="Green" title="E32">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>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c3">t</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">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="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  ;<br/>
<a NAME="E6:31"/><i><font color="Green" title="E33">A9</font></i>: 
 <a href="reloc.html#K3" title="RELOC:func.3">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#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">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="E7:31"/><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="reloc.html#E3:31"><i><font color="Green" title="E31">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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E9:31"/><i><font color="Green" title="E34">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="ami_3.html#K1" title="AMI_3:func.1">SCM</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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <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="E11:31"/>
<font color="Maroon" title="c6">s3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s3</font>
 
;<br/>
<a NAME="E12:31"/><b>then </b><i><font color="Green" title="E35">A11</font></i>: 
 <a href="reloc.html#K1" title="RELOC: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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="txt" href="reloc.html#E1:31"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="reloc.html#E4:31"><i><font color="Green" title="E32">A8</font></i></a>, <a class="txt" href="reloc.html#E6:31"><i><font color="Green" title="E33">A9</font></i></a>, <a class="txt" href="reloc.html#E9:31"><i><font color="Green" title="E34">A10</font></i></a>, <a class="ref" href="reloc.html#T34" target="_self" title="RELOC:th.34">Th34</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><br/>

<b>thus </b><a NAME="E13:31"/>
 <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="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="txt" href="reloc.html#E12:31"><i><font color="Green" title="E35">A11</font></i></a>, <a class="ref" href="reloc.html#T14" target="_self" title="RELOC:th.14">Th14</a>, <a class="ref" href="ami_5.html#T37" title="AMI_5:th.37">AMI_5:37</a></i>;<br/>


</div>
