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<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="scmfsa_2.html#K1">SCM+FSA</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="E1:15"/><i><font color="Green">E15</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</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="E1:15_1"/><i><font color="Green">E16</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="E2:15_1"/>
 <a href="scmfsa_5.html#K1" 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="15_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="scmfsa_2.html#K1">SCM+FSA</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="E1:15_1_1"/><i><font color="Green">E17</font></i>: 
 <a href="scmfsa_5.html#K1" 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="scmfsa_2.html#K1">SCM+FSA</a>  ;<br/>
<a NAME="E3:15_1_1"/><i><font color="Green">E18</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="E4:15_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="scmfsa_5.html#E1:15_1"><i><font color="Green">E16</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="E6:15_1_1"/><i><font color="Green">E19</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="scmfsa_2.html#K1">SCM+FSA</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> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> as   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <b>by </b><i><a class="ref" href="ami_5.html#T82">AMI_5:82</a></i>;<br/>
<a NAME="E8:15_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">E20</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="scmfsa_4.html#K4">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="scmfsa_5.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="scmfsa_5.html#E1:15_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmfsa_5.html#E3:15_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scmfsa_5.html#E6:15_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmfsa_5.html#T12" target="_self">Th12</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="scmfsa_4.html#T8">SCMFSA_4:8</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="E10:15_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="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E9:15_1_1"><i><font color="Green">E20</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E3:15"/><i><font color="Green">E16</font></i>: 
 <a href="scmfsa_5.html#K1" 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="scmfsa_2.html#K1">SCM+FSA</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="E4:15"/><i><font color="Green">E17</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="scmfsa_5.html#K1" 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="scmfsa_2.html#K1">SCM+FSA</a>  ;<br/>
<a NAME="E6:15"/><i><font color="Green">E18</font></i>: 
 <a href="scmfsa_5.html#K1" 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="scmfsa_5.html#K1" 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="E7:15"/><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="scmfsa_5.html#E3:15"><i><font color="Green">E16</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="E9:15"/><i><font color="Green">E19</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="scmfsa_2.html#K1">SCM+FSA</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> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> as   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <b>by </b><i><a class="ref" href="ami_5.html#T82">AMI_5:82</a></i>;<br/>
<a NAME="E11:15"/>
<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="E12:15"/><b>then </b><i><font color="Green">E20</font></i>: 
 <a href="scmfsa_4.html#K4">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="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="scmfsa_5.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmfsa_5.html#E6:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scmfsa_5.html#E9:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmfsa_5.html#T12" target="_self">Th12</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/>

<a NAME="E13:15"/><i><font color="Green">E21</font></i>: 
not 0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E14:15"/>
 <a href="ami_5.html#K1">InsCode</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> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E12:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a>, <a class="ref" href="scmfsa_4.html#T22">SCMFSA_4:22</a></i>;<br/>
<b>hence </b><a NAME="E15:15"/>
 <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="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E12:15"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmfsa_5.html#E13:15"><i><font color="Green">E21</font></i></a>, <a class="ref" href="scmfsa_4.html#D3">SCMFSA_4:def 3</a></i>;<br/>


</div>
