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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ami_5.html#V1">data-only</a>  <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green">E32</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:33"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:33"/><i><font color="Green">E34</font></i>: 
not  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">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">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/>

<a NAME="E2:33_1"/><b>then </b>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  is    <a href="ami_3.html#M1">Data-Location</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D2">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">AMI_5:20</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:33"/><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T97">AMI_5:97</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green">E36</font></i>: 
not  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="reloc.html#E3:33"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E6:33"/>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="reloc.html#E2:33"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E37</font></i>:  <a href="ami_3.html#K13">IC</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D16">AMI_3:def 16</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i><a class="txt" href="reloc.html#E2:33"><i><font color="Green">E33</font></i></a>, <a class="txt" href="reloc.html#E5:33"><i><font color="Green">E36</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
 <a href="ami_3.html#K13">IC</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="reloc.html#E1:33"><i><font color="Green">E32</font></i></a>, <a class="ref" href="ami_3.html#D16">AMI_3:def 16</a></i>
;<br/>
<a NAME="E8:33"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 
<b>by </b><i><a class="txt" href="reloc.html#E4:33"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_5.html#T33">AMI_5:33</a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<i><font color="Green">E39</font></i>:  <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
<b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a> 
<b>by </b><i><a class="txt" href="reloc.html#E8:33"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ami_3.html#D1">AMI_3:def 1</a>, <a class="ref" href="funct_4.html#T76">FUNCT_4:76</a></i>
<br/>.= 
 <a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">c<sub>2</sub></font>

;<br/>
<i><font color="Green">E40</font></i>:  <a href="ami_5.html#K7">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
<b>by </b><i><a class="ref" href="ami_5.html#T96">AMI_5:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T96">AMI_5:96</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="reloc.html#E4:33"><i><font color="Green">E35</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="reloc.html#K5" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="reloc.html#K4" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>thus </b> <a href="reloc.html#K6" target="_self">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_3.html#K13">IC</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="reloc.html#K5" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="reloc.html#K4" target="_self">Shift</a> <span class="p4">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="reloc.html#E10:33"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_3.html#K13">IC</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="reloc.html#K5" target="_self">IncAddr</a> <span class="p4">(<span class="default"><a href="reloc.html#K4" target="_self">Shift</a> <span class="p5">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="funct_4.html#T15">FUNCT_4:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="reloc.html#E7:33"><i><font color="Green">E37</font></i></a>, <a class="txt" href="reloc.html#E9:33"><i><font color="Green">E39</font></i></a></i>
;<br/>


</div>
