<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">P</font> be  <a href="ami_3.html#V1">programmed</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:6_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E2:6_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/><b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:6_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T21">SCMFSA_2:21</a></i>;<br/><b>thus </b><a NAME="E5:6_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:6_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:6_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> &amp;  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> )
 ;<br/><b>thus </b><a NAME="E5:6_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E2:6"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<a NAME="E3:6"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:6_2"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">P</font>,0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 <b>by </b><i>, <a class="ref" href="scmfsa_5.html#T3">SCMFSA_5:3</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:6_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">P</font>,0</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:6_2_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 0</span>)</span> &amp;  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> )
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E4:6_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E3:6_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:6_2"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> &amp;  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> )
 ;<br/><a NAME="E6:6_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 0</span>)</span> &amp;  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E7:6_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">P</font>,0</span>)</span></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E5:6"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">P</font>,0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:6_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:6_3"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E4:6_3"/><i><font color="Green">E51</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font>
 ;<br/><a NAME="E5:6_3"/><i><font color="Green">E52</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>;<br/><a NAME="E6:6_3"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>,0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span> </span>}</span> 
 <b>by </b><i><a class="ref" href="scmfsa_4.html#D7">SCMFSA_4:def 7</a></i>;<br/><a NAME="E7:6_3"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 0</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>,0</span>)</span>
 <b>by </b><i>, </i>;<br/><b>then </b><i><font color="Green">E54</font></i>:  <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>,0</span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>,0</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>,0</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_4.html#T30">SCMFSA_4:30</a></i>
<br/>.= 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>
;<br/><b>then consider </b><font color="Maroon">i</font> being   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E10:6_3"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">n</font></span>)</span>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">P</font>,0</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">P</font></span>)</span>,0</span>)</span>,0</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_5.html#T2">SCMFSA_5:2</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4">IncAddr</a> <font color="Maroon">i</font>,0
<b>by </b><i>, , , <a class="ref" href="scmfsa_4.html#D6">SCMFSA_4:def 6</a></i>
<br/>.= 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:6"/>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <font color="Maroon">P</font>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
