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

<b>let </b><font color="Maroon" title="c1">s</font> be  <a href="ami_5.html#V1" title="AMI_5:attr.1">data-only</a>  <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="E1:10"/><i><font color="Green" title="E11">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#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 ;<br/>

<a NAME="E2:10"/><b>then </b><i><font color="Green" title="E12">A2</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> <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="E3:10"/><i><font color="Green" title="E13">A3</font></i>: 
not  <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="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> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:10_1"/><i><font color="Green" title="E14">A4</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="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> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1_1"/>
(  <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="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a>  or  <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="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a>  )
 </span><b>by </b><i><a class="txt" href="scmfsa_5.html#E1:10_1"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1"><b>suppose </b></a><a NAME="E1:10_1_1_1"/>
 <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="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a> 
 ;<br/><div class="add"><a NAME="E2:10_1_1_1"/><b>then </b>
 <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>  is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T11" title="SCMFSA_2:th.11">SCMFSA_2:11</a></i>;<br/><b>hence </b><a NAME="E3:10_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T81" title="SCMFSA_2:th.81">SCMFSA_2:81</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_2"><b>suppose </b></a><a NAME="E1:10_1_1_2"/>
 <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="scmfsa_2.html#K3" title="SCMFSA_2:func.3">FinSeq-Locations</a> 
 ;<br/><div class="add"><a NAME="E2:10_1_1_2"/><b>then </b>
 <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>  is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T12" title="SCMFSA_2:th.12">SCMFSA_2:12</a></i>;<br/><b>hence </b><a NAME="E3:10_1_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T82" title="SCMFSA_2:th.82">SCMFSA_2:82</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E4:10"/><i><font color="Green" title="E14">A5</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="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> 
 
<b>by </b><i><a class="ref" href="scmfsa_3.html#T7" title="SCMFSA_3:th.7">SCMFSA_3:7</a></i>;<br/>
<a NAME="E5:10"/><b>then </b><i><font color="Green" title="E15">A6</font></i>: 
not  <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#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E3:10"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/>
<a NAME="E6:10"/>
 <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#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#K17" title="AMI_1:func.17">+*</a> <font color="Maroon" title="c1">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E2:10"><i><font color="Green" title="E12">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="E16">A7</font></i>:  <a href="ami_3.html#K13" title="AMI_3:func.13">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</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#K17" title="AMI_1:func.17">+*</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D16" title="AMI_3:def.16">AMI_3:def 16</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_5.html#E2:10"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="scmfsa_5.html#E5:10"><i><font color="Green" title="E15">A6</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_3.html#K13" title="AMI_3:func.13">IC</a> <font color="Maroon" title="c2">p</font>
<b>by </b><i><a class="txt" href="scmfsa_5.html#E1:10"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="ami_3.html#D16" title="AMI_3:def.16">AMI_3:def 16</a></i>
;<br/>
<a NAME="E8:10"/><i><font color="Green" title="E17">A8</font></i>: 
 <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> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E4:10"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="scmfsa_5.html#E2"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E9:10"/><i><font color="Green" title="E18">A9</font></i>: 
 <a href="ami_5.html#K6" title="AMI_5:func.6">ProgramPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_5.html#K6" title="AMI_5:func.6">ProgramPart</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E8:10"><i><font color="Green" title="E17">A8</font></i></a>, <a class="ref" href="funct_4.html#T76" title="FUNCT_4:th.76">FUNCT_4:76</a></i>;<br/>
<i><font color="Green" title="E19">A10</font></i>:  <a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</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#K17" title="AMI_1:func.17">+*</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T6" title="SCMFSA_3:th.6">SCMFSA_3:6</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> <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> <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> <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="funct_4.html#T75" title="FUNCT_4:th.75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">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> <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="scmfsa_3.html#T6" title="SCMFSA_3:th.6">SCMFSA_3:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_5.html#K7" title="AMI_5:func.7">DataPart</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <font color="Maroon" title="c1">s</font>
<b>by </b><i><a class="txt" href="scmfsa_5.html#E4:10"><i><font color="Green" title="E14">A5</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_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13" title="AMI_3:func.13">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K7" title="SCMFSA_4:func.7">IncAddr</a> <span class="p2">(<span class="default"><a href="scmfsa_4.html#K8" title="SCMFSA_4:func.8">Shift</a> <span class="p3">(<span class="default"><a href="ami_5.html#K6" title="AMI_5:func.6">ProgramPart</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</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="E11:10"/>
 <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</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="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <font color="Maroon" title="c1">s</font>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E10:10"><i><font color="Green" title="E19">A10</font></i></a>, <a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a>, <a class="txt" href="scmfsa_5.html#E7:10"><i><font color="Green" title="E16">A7</font></i></a>, <a class="txt" href="scmfsa_5.html#E9:10"><i><font color="Green" title="E18">A9</font></i></a></i>;<br/>


</div>
