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

<b>let </b><font color="Maroon" title="c1">s</font> be  <a href="ami_1.html#V16" title="AMI_1:attr.16">data-only</a> <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>let </b><font color="Maroon" title="c3">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> ;<br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E32">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#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 ;<br/>

<a NAME="E2:33"/><b>then </b><i><font color="Green" title="E33">A2</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> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:33"/><i><font color="Green" title="E34">A3</font></i>: 
not  <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="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_1"/>
 <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="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/>

<a NAME="E2:33_1"/><b>then </b>
 <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>  is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D2" title="AMI_3:def.2">AMI_3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:33_1"/>
contradiction
 <b>by </b><i><a class="ref" href="ami_5.html#T20" title="AMI_5:th.20">AMI_5:20</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:33"/><i><font color="Green" title="E35">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T97" title="AMI_5:th.97">AMI_5:97</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green" title="E36">A5</font></i>: 
not  <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#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font>
 
<b>by </b><i><a class="txt" href="reloc.html#E3:33"><i><font color="Green" title="E34">A3</font></i></a></i>;<br/>
<a NAME="E6:33"/>
 <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#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="reloc.html#E2:33"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E37">A6</font></i>:  <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><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> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D43" title="AMI_1:def.43">AMI_1:def 43</a></i>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><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> </span>)</span>
<b>by </b><i><a class="txt" href="reloc.html#E2:33"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="reloc.html#E5:33"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c2">p</font>
<b>by </b><i><a class="txt" href="reloc.html#E1:33"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="ami_1.html#D43" title="AMI_1:def.43">AMI_1:def 43</a></i>
;<br/>
<a NAME="E8:33"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> 
 
<b>by </b><i><a class="txt" href="reloc.html#E4:33"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="ami_2.html#T29" title="AMI_2:th.29">AMI_2:29</a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E9:33"/><b>then </b><i><font color="Green" title="E38">A7</font></i>: 
 <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></i>;<br/>
<i><font color="Green" title="E39">A8</font></i>:  <a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
<b>by </b><i><a class="ref" href="ami_5.html#T96" title="AMI_5:th.96">AMI_5:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T75" title="FUNCT_4:th.75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T96" title="AMI_5:th.96">AMI_5:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K32" title="AMI_1:func.32">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font>
<b>by </b><i><a class="txt" href="reloc.html#E4:33"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c4">ICP</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="reloc.html#K1" title="RELOC:func.1">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <span class="p1">(<span class="default"><a href="reloc.html#K5" title="RELOC:func.5">IncAddr</a> <span class="p2">(<span class="default"><a href="reloc.html#K4" title="RELOC:func.4">Shift</a> <span class="p3">(<span class="default"><a href="ami_1.html#K31" title="AMI_1:func.31">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span>;<br/>
<b>thus </b><a NAME="E11:33"/>
 <a href="reloc.html#K6" title="RELOC:func.6">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font></span>)</span>,<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" title="RELOC:func.6">Relocated</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</a> <font color="Maroon" title="c1">s</font>
 <b>by </b><i><a class="txt" href="reloc.html#E10:33"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a>, <a class="txt" href="reloc.html#E7:33"><i><font color="Green" title="E37">A6</font></i></a>, <a class="txt" href="reloc.html#E9:33"><i><font color="Green" title="E38">A7</font></i></a></i>;<br/>


</div>
