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

<b>let </b><font color="Maroon">p</font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">X</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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:2_1"/>
 <a href="relat_1.html#K1">dom</a> <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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:2_1"/><b>then </b>
<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"><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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E3:2_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E4:2_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:2_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_1"><b>suppose </b></a><a NAME="E1:2_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><a NAME="E3:2_1_1_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_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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:2_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="ami_3.html#T34">AMI_3:34</a></i>;<br/><a NAME="E5:2_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:2_1_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T81">SCMFSA_2:81</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="2_1_1_2"><b>suppose </b></a><a NAME="E1:2_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><a NAME="E3:2_1_1_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_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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:2_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="ami_3.html#T34">AMI_3:34</a></i>;<br/><a NAME="E5:2_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:2_1_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T82">SCMFSA_2:82</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E3:2"/><b>then </b>
<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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> is   <a href="funct_2.html#NM1">Function</a> of  <a href="xboole_0.html#K1">{}</a> , <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T55">FUNCT_2:55</a></i>;<br/>
<a NAME="E4:2"/><b>then </b><i><font color="Green">E33</font></i>: 
<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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T57">PARTFUN1:57</a></i>;<br/>
<a NAME="E5:2"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <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>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <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/>
<a NAME="E6:2"/><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_3.html#T8">SCMFSA_3:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">kk</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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon">rr</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p4">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></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">p</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>thus </b> <a href="ami_5.html#K7">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> = 
<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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p4">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p5">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</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">p</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T6">SCMFSA_3:6</a></i>
<br/>.= 
<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> <font color="Maroon">p</font></span>)</span> <a href="scmfsa_4.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p4">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p5">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T15">FUNCT_4:15</a></i>
<br/>.= 
<font color="Maroon">kk</font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">rr</font>
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_4.html#K7">IncAddr</a> <span class="p3">(<span class="default"><a href="scmfsa_4.html#K8">Shift</a> <span class="p4">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <font color="Maroon">p</font></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></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">p</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T21">FUNCT_4:21</a></i>
<br/>.= 
 <a href="ami_5.html#K7">DataPart</a> <font color="Maroon">p</font>
<b>by </b><i>, , , <a class="ref" href="funct_4.html#T81">FUNCT_4:81</a></i>
;<br/>


</div>
