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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/>



<b>assume </b><a NAME="E1:71"/><i><font color="Green">E55</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="ami_1.html#V11">autonomic</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E2:71"/><i><font color="Green">E56</font></i>: 
 <a href="ami_1.html#K2">IC</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:71_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="ami_1.html#V12">halting</a>
 ;<br/><b>thus </b><a NAME="E2:71_1"/>
 <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="ami_1.html#V12">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">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>; <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="E1:71_1_1"/><i><font color="Green">E58</font></i>: 
 <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E2:71_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E3:71_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>3</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:71_1"><i><font color="Green">E57</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>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:71_1_1"/><i><font color="Green">E60</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> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <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>7</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="ami_5.html#T82">AMI_5:82</a></i>;<br/>
<a NAME="E7:71_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
;<br/>
<b>then </b><i><font color="Green">E61</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>6</sub></font></span>)</span> = 
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="scmring4.html#E1:71"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmring4.html#E2:71"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmring4.html#E1:71_1_1"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmring4.html#E2:71_1_1"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmring4.html#E5:71_1_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmring4.html#T59" target="_self">Th59</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>
;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</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="E9:71_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>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E8:71_1_1"><i><font color="Green">E61</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">E57</font></i>: 
 <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> is <a href="ami_1.html#V12">halting</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>; <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="E5:71"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> as   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ;<br/>
<a NAME="E7:71"/><i><font color="Green">E59</font></i>: 
 <a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmring4.html#K3" target="_self">Relocated</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E8:71"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="txt" href="scmring4.html#E4:71"><i><font color="Green">E57</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>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:71"/><i><font color="Green">E60</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>5</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <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>7</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>5</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 <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="ami_5.html#T82">AMI_5:82</a></i>;<br/>
<a NAME="E12:71"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
;<br/>
<a NAME="E13:71"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="amistd_2.html#K8">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>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmring4.html#E1:71"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmring4.html#E2:71"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmring4.html#E5:71"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmring4.html#E7:71"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmring4.html#E10:71"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmring4.html#T59" target="_self">Th59</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</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="E14:71"/>
 <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>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E13:71"><i><font color="Green">E61</font></i></a>, <a class="ref" href="amistd_2.html#T35">AMISTD_2:35</a></i>;<br/>


</div>
