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

<b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font>, <font color="Maroon" title="c5">J</font> be  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a> <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</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> ;<br/>





<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E40">A1</font></i>: 
( <font color="Maroon" title="c4">I</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">does_not_refer</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c5">J</font> <a href="scmfsa7b.html#R2" title="SCMFSA7B:pred.2">does_not_refer</a> <font color="Maroon" title="c6">a</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c8">i</font> =  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">II</font> =  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Macro</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span> as  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a> <a href="scmfsa6b.html#V3" title="SCMFSA6B:attr.3">keeping_0</a> <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">JJ</font> =  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font> as  <a href="scmfsa6b.html#V2" title="SCMFSA6B:attr.2">parahalting</a> <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a> ;<br/>
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font> = 
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">II</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <font color="Maroon" title="c10">JJ</font></span>)</span>,<font color="Maroon" title="c3">s</font>
<b>by </b><i><a class="ref" href="scmfsa6a.html#D5" title="SCMFSA6A:def.5">SCMFSA6A:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c9">II</font>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span> <a href="ami_1.html#K33" title="AMI_1:func.33">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p5">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c9">II</font>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">II</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6b.html#T44" title="SCMFSA6B:th.44">SCMFSA6B:44</a></i>
;<br/>
<b>hence </b> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p3">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c9">II</font>,<font color="Maroon" title="c3">s</font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">II</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T111" title="AMI_1:th.111">AMI_1:111</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c9">II</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> 2
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" title="SCMFSA7B:th.6">SCMFSA7B:6</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D1" title="SCMFSA_4:def.1">SCMFSA_4:def 1</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c5">J</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span>

;<br/><br/>

<b>set </b><font color="Maroon" title="c11">s1</font> =  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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>;<br/>
<b>set </b><font color="Maroon" title="c12">s2</font> = <font color="Maroon" title="c3">s</font>;<br/>
<div><i><font color="Green" title="E41">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">c</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> ;<br/><b>assume </b><a NAME="E1:50_3"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">c</font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">c</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">c</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E42">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="50_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</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="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</a></i>
<br/>.= 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
;<br/></div><b>end;</b></div>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:50_5"/><i><font color="Green" title="E43">A4</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font>
 ;<br/><i><font color="Green" title="E44">A5</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:50_5"><i><font color="Green" title="E43">A4</font></i></a></i>
;<br/><a NAME="E3:50_5"/><i><font color="Green" title="E45">A6</font></i>: 
( <font color="Maroon" title="c4">I</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> &amp; <font color="Maroon" title="c4">I</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> )
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T24" title="SCMFSA7B:th.24">SCMFSA7B:24</a>, <a class="ref" href="scmfsa7b.html#T25" title="SCMFSA7B:th.25">SCMFSA7B:25</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c13">d</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:50_5_2"/><i><font color="Green" title="E46">A7</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 ;<br/><b>thus </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="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T12" target="_self" title="SCMFSA8B:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:50_5"><i><font color="Green" title="E44">A5</font></i></a>, <a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:50"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:50"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:50"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:50_5"><i><font color="Green" title="E45">A6</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:50_5_2"><i><font color="Green" title="E46">A7</font></i></a>, <a class="ref" href="scmfsa8b.html#T41" target="_self" title="SCMFSA8B:th.41">Th41</a></i>
;<br/></div>
<b>end;</b></div><b>let </b><font color="Maroon" title="c13">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/><b>thus </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="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T13" target="_self" title="SCMFSA8B:th.13">Th13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c4">I</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E2:50_5"><i><font color="Green" title="E44">A5</font></i></a>, <a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:50"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:50"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:50"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="scmfsa8b.html#E3:50_5"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="scmfsa8b.html#T41" target="_self" title="SCMFSA8B:th.41">Th41</a></i>
;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E9:50"/><i><font color="Green" title="E43">A8</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font>
 ;<br/>

<i><font color="Green" title="E44">A9</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T91" title="SCMFSA_2:th.91">SCMFSA_2:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></i>
;<br/>
<a NAME="E11:50"/><i><font color="Green" title="E45">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c7">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8b.html#E9:50"><i><font color="Green" title="E43">A8</font></i></a></i>;<br/>
<a NAME="E12:50"/><i><font color="Green" title="E46">A11</font></i>: 
( <font color="Maroon" title="c5">J</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> &amp; <font color="Maroon" title="c5">J</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span> )
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T24" title="SCMFSA7B:th.24">SCMFSA7B:24</a>, <a class="ref" href="scmfsa7b.html#T25" title="SCMFSA7B:th.25">SCMFSA7B:25</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c13">d</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:50_7"/><i><font color="Green" title="E47">A12</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 ;<br/><b>thus </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="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T12" target="_self" title="SCMFSA8B:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c5">J</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E10:50"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="scmfsa8b.html#E11:50"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:50"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:50"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:50"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="scmfsa8b.html#E12:50"><i><font color="Green" title="E46">A11</font></i></a>, <a class="txt" href="scmfsa8b.html#E1:50_7"><i><font color="Green" title="E47">A12</font></i></a>, <a class="ref" href="scmfsa8b.html#T41" target="_self" title="SCMFSA8B:th.41">Th41</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c13">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/>

<b>thus </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="scmfsa8b.html#K4" title="SCMFSA8B:func.4">if=0</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">J</font></span>)</span>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c10">JJ</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T13" target="_self" title="SCMFSA8B:th.13">Th13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c5">J</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span>)</span>,<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E10:50"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="scmfsa8b.html#E11:50"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> <font color="Maroon" title="c5">J</font>,<font color="Maroon" title="c3">s</font></span>)</span> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c13">f</font>
<b>by </b><i><a class="txt" href="scmfsa8b.html#E1:50"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="scmfsa8b.html#E6:50"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="scmfsa8b.html#E7:50"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="scmfsa8b.html#E12:50"><i><font color="Green" title="E46">A11</font></i></a>, <a class="ref" href="scmfsa8b.html#T41" target="_self" title="SCMFSA8B:th.41">Th41</a></i>
;<br/>


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