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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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS: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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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="E1:18"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS: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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS: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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:18"/><i><font color="Green" title="E19">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="E4:18"/>
<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="#E3:18"><i><font color="Green" title="E19">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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:18"/><i><font color="Green" title="E20">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="E7:18"/><i><font color="Green" title="E21">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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E9:18"/><i><font color="Green" title="E22">A5</font></i>: 
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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/>
<b>reconsider </b><font color="Maroon" title="c6">s3</font> = <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <font color="Maroon" title="c5">t</font></span>)</span> as   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ;<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="scmfsa_4.html#K1" title="SCMFSA_4: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="#E1:18"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="#E3:18"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="#E9:18"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="scmfsa_5.html#T12" target="_self" title="SCMFSA_5:th.12">Th12</a></i>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="txt" href="#E6:18"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="#E7:18"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="scmfsa_4.html#T8" title="SCMFSA_4:th.8">SCMFSA_4:8</a></i>
;<br/>
<a NAME="E12:18"/><b>then </b><i><font color="Green" title="E23">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="E13:18"/><i><font color="Green" title="E24">A9</font></i>: 
(  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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="#E1:18"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="scmfsa_5.html#T13" target="_self" title="SCMFSA_5:th.13">Th13</a>, <a class="ref" href="scmfsa_5.html#T16" target="_self" title="SCMFSA_5:th.16">Th16</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> = 
 <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <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="card_3.html#K11" title="CARD_3:func.11">|</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>
<b>by </b><i><a class="txt" href="#E3:18"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="ami_1.html#D28" title="AMI_1:def.28">AMI_1:def 28</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="card_3.html#K11" title="CARD_3:func.11">|</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> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a>, <a class="ref" href="scmfsa_2.html#T127" title="SCMFSA_2:th.127">SCMFSA_2:127</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="card_3.html#K11" title="CARD_3:func.11">|</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="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a>, <a class="ref" href="scmfsa_2.html#T127" title="SCMFSA_2:th.127">SCMFSA_2:127</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="card_3.html#K11" title="CARD_3:func.11">|</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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:18"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="#E12:18"><i><font color="Green" title="E23">A7</font></i></a>, <a class="txt" href="#E1:18"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="#E3:18"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="#E9:18"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="scmfsa_5.html#T12" target="_self" title="SCMFSA_5:th.12">Th12</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="card_3.html#K11" title="CARD_3:func.11">|</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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <a href="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a>, <a class="ref" href="scmfsa_2.html#T127" title="SCMFSA_2:th.127">SCMFSA_2:127</a></i>
<br/>.= 
 <a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <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="card_3.html#K11" title="CARD_3:func.11">|</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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a>, <a class="ref" href="scmfsa_2.html#T127" title="SCMFSA_2:th.127">SCMFSA_2:127</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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">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="#E9:18"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="#E13:18"><i><font color="Green" title="E24">A9</font></i></a>, <a class="ref" href="ami_1.html#D28" title="AMI_1:def.28">AMI_1:def 28</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>
