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

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <br/> for <font color="Olive" title="b2">Ig</font> being  <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st (  <a href="scmfsa9a.html#R1" title="SCMFSA9A:pred.1">ProperBodyWhile=0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">Ig</font>,<font color="Maroon" title="c3">s</font> or <font color="Olive" title="b2">Ig</font> is  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  ) &amp; <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>for <font color="Olive" title="b3">k</font> being   <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>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Ig</font> being  <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st (  <a href="scmfsa9a.html#R1" title="SCMFSA9A:pred.1">ProperBodyWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">Ig</font>,<font color="Maroon" title="c3">s</font> or <font color="Olive" title="b1">Ig</font> is  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  ) &amp; <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>for <font color="Olive" title="b2">k</font> being   <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>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><span class="kw">let </span><font color="Maroon" title="c5">Ig</font> be   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( (  <a href="scmfsa9a.html#R1" title="SCMFSA9A:pred.1">ProperBodyWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font> or <font color="Maroon" title="c5">Ig</font> is  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  ) &amp; <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies for <font color="Olive" title="b1">k</font> being   <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>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">I</font> = <font color="Maroon" title="c5">Ig</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:29"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
(  <a href="scmfsa9a.html#R1" title="SCMFSA9A:pred.1">ProperBodyWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font> or <font color="Maroon" title="c5">Ig</font> is  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a>  )
 <span class="kw">and </span><br/><a NAME="E2:29"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being   <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>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">SW</font> =  <a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> $1</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1;<br/>
<a NAME="E3:29"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
for <font color="Olive" title="b1">k</font> being   <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>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:29_1"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:29_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:29_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><a NAME="E2:29_1_1_1"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa9a.html#T24" target="_self" title="SCMFSA9A:th.24">Th24</a></span>;<br/><span class="kw">hence </span><a NAME="E3:29_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:29_1_1_2"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c9">Ins</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><span class="kw">set </span><font color="Maroon" title="c10">IS</font> = <font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c11">SWkIS</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</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="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>;<br/><a NAME="E2:29_1_1_2"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T13" title="SCMFSA_2:th.13">SCMFSA_2:13</a>, <a class="ref" href="scmfsa_2.html#T14" title="SCMFSA_2:th.14">SCMFSA_2:14</a>, <a class="ref" href="xboole_1.html#T70" title="XBOOLE_1:th.70">XBOOLE_1:70</a></span>;<br/><a NAME="E3:29_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A6</font></span>: 
 <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"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</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> </span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#T3" title="SCMFSA8A:th.3">SCMFSA8A:3</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">SWkI</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c13">ISWk</font> =  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span>;<br/><a NAME="E4:29_1_1_2"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="scmfsa8c.html#T27" title="SCMFSA8C:th.27">SCMFSA8C:27</a></span>;<br/><a NAME="E5:29_1_1_2"/><span class="lab"><font color="Green" title="E30">A8</font></span>: 
 <a href="scmfsa9a.html#R1" title="SCMFSA9A:pred.1">ProperBodyWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="scmfsa9a.html#T19" target="_self" title="SCMFSA9A:th.19">Th19</a></span>;<br/><a NAME="E6:29_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A9</font></span>: 
<font color="Maroon" title="c5">Ig</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1_1_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="scmfsa9a.html#D1" target="_self" title="SCMFSA9A:def.1">Def1</a></span>;<br/><a NAME="E7:29_1_1_2"/>
<font color="Maroon" title="c5">Ig</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1_1_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="txt" href="#E5:29_1_1_2"><span class="lab"><font color="Green" title="E30">A8</font></span></a>, <a class="ref" href="scmfsa9a.html#D1" target="_self" title="SCMFSA9A:def.1">Def1</a></span>;<br/><a NAME="E8:29_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A10</font></span>: 
<font color="Maroon" title="c5">Ig</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:29_1_1_2"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E4:29_1_1_2"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="scmfsa8b.html#T8" title="SCMFSA8B:th.8">SCMFSA8B:8</a></span>;<br/><a NAME="E9:29_1_1_2"/><span class="kw">then </span>
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <span class="p1">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8c.html#T22" title="SCMFSA8C:th.22">SCMFSA8C:22</a></span>;<br/><a NAME="E10:29_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">X</font></span>: 
(  <a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font> &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></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="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</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#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</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#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#T4" title="SCMFSA6B:th.4">SCMFSA6B:4</a>, <a class="ref" href="scmfsa7b.html#D8" title="SCMFSA7B:def.8">SCMFSA7B:def 8</a></span>;<br/><a NAME="E11:29_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</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#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></span>;<br/><a NAME="E12:29_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A11</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span></span>)</span> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:29_1_1_2"><span class="lab"><font color="Green" title="E33">X</font></span></a></span>;<br/><a NAME="E13:29_1_1_2"/><span class="lab"><font color="Green" title="E35">A12</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</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="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="scmfsa8c.html#T18" title="SCMFSA8C:th.18">SCMFSA8C:18</a></span>;<br/><span class="lab"><font color="Green" title="E36">A13</font></span>:  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c5">Ig</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span></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"><span class="p4">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</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> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#D1" title="SCMFSA6B:def.1">SCMFSA6B:def 1</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c5">Ig</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29_1_1_2"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="ref" href="funct_4.html#T94" title="FUNCT_4:th.94">FUNCT_4:94</a>, <a class="ref" href="scmfsa_2.html#T127" title="SCMFSA_2:th.127">SCMFSA_2:127</a></span>
<br/>.= 
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:29_1_1_2"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="txt" href="#E12:29_1_1_2"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></span>
;<br/><a NAME="E15:29_1_1_2"/>
<font color="Maroon" title="c5">Ig</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6c.html#K1" title="SCMFSA6C:func.1">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:29_1_1_2"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E4:29_1_1_2"><span class="lab"><font color="Green" title="E29">A7</font></span></a>, <a class="ref" href="scmfsa8b.html#T6" title="SCMFSA8B:th.6">SCMFSA8B:6</a></span>;<br/><a NAME="E16:29_1_1_2"/><span class="kw">then </span>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c5">Ig</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E1:29_1_1_2"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="txt" href="#E8:29_1_1_2"><span class="lab"><font color="Green" title="E32">A10</font></span></a>, <a class="ref" href="scmfsa9a.html#T25" target="_self" title="SCMFSA9A:th.25">Th25</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_9.html#K4" title="SCMFSA_9:func.4">StepWhile=0</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">Ig</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c8">k</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">Ig</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K18" title="AMI_1:func.18">Start-At</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:29_1_1_2"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="scmfsa6a.html#T38" title="SCMFSA6A:th.38">SCMFSA6A:38</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E6:29_1_1_2"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="ref" href="scmfsa8c.html#T97" title="SCMFSA8C:th.97">SCMFSA8C:97</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E4:29"/><span class="lab"><font color="Green" title="E26">A14</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="scmfsa_9.html#D4" title="SCMFSA_9:def.4">SCMFSA_9:def 4</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:29"/>
for <font color="Olive" title="b1">k</font> being   <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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E25">A3</font></span></a>);</span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
