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

<b>set </b><font color="Maroon" title="c1">A</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>
<b>set </b><font color="Maroon" title="c2">D</font> = <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/>
<b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c4">s1</font> = <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:29"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T13" title="SCMFSA8A:th.13">SCMFSA8A:13</a></i>;<br/>
<b>then </b> <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a>, <a class="ref" href="scmfsa6b.html#T34" title="SCMFSA6B:th.34">SCMFSA6B:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T26" target="_self" title="SCMFSA8C:th.26">Th26</a>, <a class="ref" href="scmfsa8a.html#T15" title="SCMFSA8A:th.15">SCMFSA8A:15</a></i>
;<br/>
<a NAME="E3:29"/><b>then </b><i><font color="Green" title="E26">A2</font></i>: 
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  &amp; <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="ami_1.html#T13" title="AMI_1:th.13">AMI_1:13</a>, <a class="ref" href="scmfsa8a.html#T16" title="SCMFSA8A:th.16">SCMFSA8A:16</a></i>;<br/>
<a NAME="E4:29"/><b>then </b><i><font color="Green" title="E27">A3</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V8" title="AMI_1:attr.8">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D20" title="AMI_1:def.20">AMI_1:def 20</a></i>;<br/>
<a NAME="E5:29"/><i><font color="Green" title="E28">A4</font></i>: 
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <span class="p4">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1" title="SCMFSA6B:def.1">SCMFSA6B:def 1</a></i>;<br/>
<a NAME="E6:29"/><b>then </b><i><font color="Green" title="E29">A5</font></i>: 
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="#E3:29"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="#E4:29"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="ami_1.html#D22" title="AMI_1:def.22">AMI_1:def 22</a></i>;<br/>
<b>then </b><i><font color="Green" title="E30">A6</font></i>:  <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> = 
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T37" target="_self" title="SCMFSA8C:th.37">Th37</a></i>
<br/>.= 
 <a href="scmnorm.html#K15" title="SCMNORM:func.15">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8a.html#T11" title="SCMFSA8A:th.11">SCMFSA8A:11</a></i>
;<br/>
<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span>
<div class="add"><i><font color="Green" title="E31">A7</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>
<br/>.= 
 <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="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>
;<br/><a NAME="E2:29_3"/><i><font color="Green" title="E32">A8</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#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> implies <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><b>assume </b><a NAME="E1:29_3_2"/><i><font color="Green" title="E33">A9</font></i>: 
<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="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_3_2_1"/>
( <font color="Maroon" title="c5">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  or <font color="Maroon" title="c5">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  or <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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  or <font color="Maroon" title="c5">x</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  )
 </span><b>by </b><i><a class="txt" href="#E1:29_3_2"><i><font color="Green" title="E33">A9</font></i></a>, <a class="ref" href="scmfsa6a.html#T35" title="SCMFSA6A:th.35">SCMFSA6A:35</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_3_2_1_1"><b>suppose </b></a><a NAME="E1:29_3_2_1_1"/><i><font color="Green" title="E34">A10</font></i>: 
<font color="Maroon" title="c5">x</font> is    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:29_3_2_1_1"/><b>then </b><i><font color="Green" title="E35">A11</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E7:29"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></i>;<br/><a NAME="E3:29_3_2_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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> 
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_1"><i><font color="Green" title="E34">A10</font></i></a>, <a class="ref" href="scmfsa_2.html#T81" title="SCMFSA_2:th.81">SCMFSA_2:81</a></i>;<br/><a NAME="E4:29_3_2_1_1"/><b>then </b>
not <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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:29_3"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:29_3_2_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E2:29_3_2_1_1"><i><font color="Green" title="E35">A11</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_3_2_1_2"><b>suppose </b></a><a NAME="E1:29_3_2_1_2"/><i><font color="Green" title="E34">A12</font></i>: 
<font color="Maroon" title="c5">x</font> is    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:29_3_2_1_2"/><b>then </b><i><font color="Green" title="E35">A13</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E7:29"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></i>;<br/><a NAME="E3:29_3_2_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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> 
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_2"><i><font color="Green" title="E34">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T82" title="SCMFSA_2:th.82">SCMFSA_2:82</a></i>;<br/><a NAME="E4:29_3_2_1_2"/><b>then </b>
not <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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:29_3"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:29_3_2_1_2"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E2:29_3_2_1_2"><i><font color="Green" title="E35">A13</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_3_2_1_3"><b>suppose </b></a><a NAME="E1:29_3_2_1_3"/><i><font color="Green" title="E34">A14</font></i>: 
<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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:29_3_2_1_3"/><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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:29_3_2_1_3"/><b>then </b><i><font color="Green" title="E35">A15</font></i>: 
<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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_3_2_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:29_3_2_1_3_1"/><i><font color="Green" title="E36">A16</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>then reconsider </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c5">x</font> as    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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="E3:29_3_2_1_3_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_3_1"><i><font color="Green" title="E36">A16</font></i></a></i>;<br/><b>hence </b><a NAME="E4:29_3_2_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_3"><i><font color="Green" title="E34">A14</font></i></a>, <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="E5:29_3_2_1_3"/><b>then </b>
not <font color="Maroon" title="c5">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> <font color="Maroon" title="c3">s</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:29_3_2_1_3"/><b>then </b>
( <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"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span> &amp; not <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"><font color="Maroon" title="c3">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_3"><i><font color="Green" title="E34">A14</font></i></a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a>, <a class="ref" href="scmfsa8b.html#T1" title="SCMFSA8B:th.1">SCMFSA8B:1</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></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="txt" href="#E6:29"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="#E1:29_3_2_1_3"><i><font color="Green" title="E34">A14</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></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="funct_4.html#T15" title="FUNCT_4:th.15">FUNCT_4:15</a></i>
<br/>.= 
<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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></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="txt" href="#E1:29_3_2_1_3"><i><font color="Green" title="E34">A14</font></i></a>, <a class="txt" href="#E3:29_3_2_1_3"><i><font color="Green" title="E35">A15</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="txt" href="#E1:29_3_2_1_3"><i><font color="Green" title="E34">A14</font></i></a>, <a class="txt" href="#E3:29_3_2_1_3"><i><font color="Green" title="E35">A15</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
;<br/> <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_3_2_1_4"><b>suppose </b></a><a NAME="E1:29_3_2_1_4"/><i><font color="Green" title="E34">A17</font></i>: 
<font color="Maroon" title="c5">x</font> is    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  = 
<font color="Maroon" title="c3">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<b>by </b><i><a class="txt" href="#E5:29"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="card_3.html#T99" title="CARD_3:th.99">CARD_3:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T36" target="_self" title="SCMFSA8C:th.36">Th36</a></i>
;<br/><a NAME="E3:29_3_2_1_4"/><b>then </b><i><font color="Green" title="E35">A18</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_4"><i><font color="Green" title="E34">A17</font></i></a>, <a class="ref" href="scmfsa6a.html#T36" title="SCMFSA6A:th.36">SCMFSA6A:36</a></i>;<br/><a NAME="E4:29_3_2_1_4"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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> 
 <b>by </b><i><a class="txt" href="#E1:29_3_2_1_4"><i><font color="Green" title="E34">A17</font></i></a>, <a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>;<br/><a NAME="E5:29_3_2_1_4"/><b>then </b>
not <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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:29_3"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:29_3_2_1_4"/>
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="#E3:29_3_2_1_4"><i><font color="Green" title="E35">A18</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</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></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:29_3"/>
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K6" title="SCMNORM:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</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"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:29_3"><i><font color="Green" title="E31">A7</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</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>


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