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

<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds   <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Olive" title="b1">k</font></span>)</span>,<font color="Olive" title="b1">k</font></span><br/><b>let </b><font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font></span><br/>



<b>set </b><font color="Maroon" title="c3">X</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></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">NAT</a> ;<br/>
<b>consider </b><font color="Maroon" title="c4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></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">NAT</a> </span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></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">NAT</a> </span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:16_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></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">NAT</a> </span>)</span>
 ;<br/><a NAME="E3:16_1"/><b>then </b><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/><a NAME="E4:16_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c4">x</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E6:16_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="reloc.html#E3:16_1"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E7:16_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<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></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E8:16_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> 
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E9:16_1"/>
contradiction
 <b>by </b><i><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E3:16"/><b>then </b><i><font color="Green" title="E16">A2</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></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">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T55" title="FUNCT_2:th.55">FUNCT_2:55</a></i>;<br/>
<a NAME="E4:16"/><i><font color="Green" title="E17">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<a NAME="E5:16"/><i><font color="Green" title="E18">A4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T87" title="RELAT_1:th.87">RELAT_1:87</a>, <a class="ref" href="ami_3.html#T72" title="AMI_3:th.72">AMI_3:72</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">SA</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></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">NAT</a>  as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">SC</font> =  <a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">SB</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">SC</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span></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">NAT</a>  as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<b>thus </b> <a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <span class="p1">(<span class="default"><a href="reloc.html#K3" title="RELOC:func.3">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmnorm.html#K2" title="SCMNORM:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p5">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span></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">NAT</a> 
<b>by </b><i><a class="ref" href="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>
<br/>.= 
<font color="Maroon" title="c5">SA</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c7">SB</font>
<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"><span class="p2">(<span class="default"><a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K35" title="AMI_1:func.35">DataPart</a> <font color="Maroon" title="c1">p</font></span>)</span></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">NAT</a> 
<b>by </b><i><a class="txt" href="reloc.html#E3:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="funct_4.html#T21" title="FUNCT_4:th.21">FUNCT_4:21</a></i>
<br/>.= 
 <a href="reloc.html#K2" title="RELOC:func.2">IncAddr</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K5" title="SCMNORM:func.5">Shift</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K8" title="SCMNORM:func.8">ProgramPart</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="reloc.html#E4:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="reloc.html#E5:16"><i><font color="Green" title="E18">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="funct_4.html#T81" title="FUNCT_4:th.81">FUNCT_4:81</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
