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<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#V11" title="AMI_1:attr.11">halting</a> <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> implies for <font color="Olive" title="b1">k</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>  holds   <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p2">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">k</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E34">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</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>  holds   <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p2">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">k</font></span>)</span></span>)</span></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p2">(<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></span>)</span></span><br/>

<b>consider </b><font color="Maroon" title="c3">s</font> being   <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> such that </b><br/><a NAME="E3:33"/><i><font color="Green" title="E35">A2</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">s</font>
 <b>by </b><i><a class="ref" href="card_3.html#T97" title="CARD_3:th.97">CARD_3:97</a></i>;<br/>
<a NAME="E4:33"/>
<font color="Maroon" title="c3">s</font> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="txt" href="#E3:33"><i><font color="Green" title="E35">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="c4">j1</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="E6:33"/><i><font color="Green" title="E36">A3</font></i>: 
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">j1</font>
 <b>and </b><br/><a NAME="E7:33"/><i><font color="Green" title="E37">A4</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#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</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#D22" title="AMI_1:def.22">AMI_1:def 22</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">t</font> being   <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> such that </b><br/><a NAME="E9:33"/><i><font color="Green" title="E38">A5</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="c5">t</font>
 <b>by </b><i><a class="ref" href="card_3.html#T97" title="CARD_3:th.97">CARD_3:97</a></i>;<br/>
<font color="Maroon" title="c5">t</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">j1</font></span>)</span></span>)</span> = 
 <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="c5">t</font>,<font color="Maroon" title="c4">j1</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <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">s</font>,<font color="Maroon" title="c4">j1</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="#E3:33"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E9:33"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="reloc.html#T35" target="_self" title="RELOC:th.35">Th34B</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="txt" href="#E6:33"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="#E7:33"><i><font color="Green" title="E37">A4</font></i></a>, <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/>
<a NAME="E11:33"/><b>then </b><i><font color="Green" title="E39">A7</font></i>: 
 <a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c5">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">j1</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T56" title="AMI_1:th.56">AMI_1:56</a></i>;<br/>
<a NAME="E12:33"/><i><font color="Green" title="E40">A8</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">j1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p3">(<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></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">s</font>,<font color="Maroon" title="c4">j1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="#E3:33"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="#E9:33"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="reloc.html#T36" target="_self" title="RELOC:th.36">Th34C</a></i>;<br/>
<a NAME="E13:33"/><i><font color="Green" title="E41">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> is <a href="ami_1.html#V11" title="AMI_1:attr.11">halting</a> &amp;  <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#V10" title="AMI_1:attr.10">autonomic</a> )
 
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="reloc.html#T38" target="_self" title="RELOC:th.38">Th35</a>, <a class="ref" href="reloc.html#T41" target="_self" title="RELOC:th.41">Th38</a></i>;<br/>
<b>thus </b> <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <font color="Maroon" title="c1">p</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <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> 
<b>by </b><i><a class="txt" href="#E3:33"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="ami_1.html#D28" title="AMI_1:def.28">AMI_1:def 28</a>, <a class="ref" href="ami_3.html#T72" title="AMI_3:th.72">AMI_3:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T72" title="AMI_3:th.72">AMI_3:72</a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E6:33"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="#E11:33"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="#E12:33"><i><font color="Green" title="E40">A8</font></i></a>, <a class="ref" href="ami_3.html#T72" title="AMI_3:th.72">AMI_3:72</a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c5">t</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<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></span>)</span></span>)</span> <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> 
<b>by </b><i><a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></i>
<br/>.= 
 <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p2">(<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></span>)</span>
<b>by </b><i><a class="txt" href="#E9:33"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="#E13:33"><i><font color="Green" title="E41">A9</font></i></a>, <a class="ref" href="ami_1.html#D28" title="AMI_1:def.28">AMI_1:def 28</a>, <a class="ref" href="ami_3.html#T72" title="AMI_3:th.72">AMI_3:72</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
