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

<b>let </b><font color="Maroon" title="c1">g</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">c</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>let </b><font color="Maroon" title="c4">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> ;<br/>







<b>reconsider </b><font color="Maroon" title="c5">mk</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c6">ml</font> = <font color="Maroon" title="c3">c</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#D4" target="_self" title="SCMFSA_2:def.4">Def4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">p</font> = <font color="Maroon" title="c1">g</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#D5" target="_self" title="SCMFSA_2:def.5">Def5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c3">c</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">S</font> = <font color="Maroon" title="c4">s</font> as   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">J</font> = 10 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13 <b>by </b><i><a class="ref" href="gr_cy_1.html#T10" title="GR_CY_1:th.10">GR_CY_1:10</a></i>;<br/>
<a NAME="E6:72"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">J</font>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c6">ml</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">mk</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
;<br/>
<a NAME="E7:72"/><i><font color="Green" title="E51">A2</font></i>: 
 <a href="ami_1.html#NK19" title="AMI_1:NK.19">InsCode</a> <font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E8:72"/><i><font color="Green" title="E52">A3</font></i>: 
<font color="Maroon" title="c8">I</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c6">ml</font>,<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">mk</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">F</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> , <font color="Maroon" title="c12">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> <b> such that </b><br/><a NAME="E10:72"/><i><font color="Green" title="E53">A4</font></i>: 
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">S</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E11:72"/><i><font color="Green" title="E54">A5</font></i>: 
<font color="Maroon" title="c11">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">S</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c12">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">S</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E12:72"/><i><font color="Green" title="E55">A6</font></i>: 
 <a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c8">I</font>,<font color="Maroon" title="c9">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c9">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c9">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E7:72"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="scmfsa_1.html#D17" title="SCMFSA_1:def.17">SCMFSA_1:def 17</a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">S1</font> =  <a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c9">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">F</font>;<br/>
<a NAME="E13:72"/><i><font color="Green" title="E56">A7</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c9">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c9">S</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E12:72"><i><font color="Green" title="E55">A6</font></i></a>, <a class="ref" href="scmfsa_1.html#D18" title="SCMFSA_1:def.18">SCMFSA_1:def 18</a></i>;<br/>
<a NAME="E14:72"/><i><font color="Green" title="E57">A8</font></i>: 
( <font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">ml</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">mk</font> )
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:72"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:72"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="scmfsa_1.html#D10" title="SCMFSA_1:def.10">SCMFSA_1:def 10</a>, <a class="ref" href="scmfsa_1.html#D11" title="SCMFSA_1:def.11">SCMFSA_1:def 11</a></i>;<br/>
<b>thus </b><a NAME="E15:72"/>
<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"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#NK1" title="SCMNORM:NK.1">Next</a> 
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E13:72"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="scmfsa_2.html#T7" target="_self" title="SCMFSA_2:th.7">Th7</a>, <a class="ref" href="scmfsa_1.html#T20" title="SCMFSA_1:th.20">SCMFSA_1:20</a></i>;<br/>

<a NAME="E16:72"/><i><font color="Green" title="E58">A9</font></i>: 
<font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:72"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:72"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="scmfsa_1.html#D12" title="SCMFSA_1:def.12">SCMFSA_1:def 12</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon" title="c14">k</font> = <font color="Maroon" title="c12">k</font>;<br/><b>thus </b><a NAME="E1:72_1"/>
<font color="Maroon" title="c14">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c2">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E6:72"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="scmfsa_2.html#E8:72"><i><font color="Green" title="E52">A3</font></i></a>, <a class="txt" href="scmfsa_2.html#E10:72"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="scmfsa_1.html#D11" title="SCMFSA_1:def.11">SCMFSA_1:def 11</a></i>;<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"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c1">g</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c9">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">F</font></span>)</span> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Maroon" title="c7">p</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E13:72"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="scmfsa_1.html#T22" title="SCMFSA_1:th.22">SCMFSA_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c1">g</font></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c14">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c3">c</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E11:72"><i><font color="Green" title="E54">A5</font></i></a>, <a class="txt" href="scmfsa_2.html#E14:72"><i><font color="Green" title="E57">A8</font></i></a>, <a class="txt" href="scmfsa_2.html#E16:72"><i><font color="Green" title="E58">A9</font></i></a>, <a class="ref" href="scmfsa_1.html#T29" title="SCMFSA_1:th.29">SCMFSA_1:29</a></i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c14">b</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>reconsider </b><font color="Maroon" title="c15">mn</font> = <font color="Maroon" title="c14">b</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#D4" target="_self" title="SCMFSA_2:def.4">Def4</a></i>;<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"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">b</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c9">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">F</font></span>)</span> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <font color="Maroon" title="c15">mn</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E13:72"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="scmfsa_1.html#T21" title="SCMFSA_1:th.21">SCMFSA_1:21</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c14">b</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T31" title="SCMFSA_1:th.31">SCMFSA_1:31</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c14">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/>

<b>assume </b><a NAME="E19:72"/><i><font color="Green" title="E59">A10</font></i>: 
<font color="Maroon" title="c14">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">g</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c15">q</font> = <font color="Maroon" title="c14">f</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#D5" target="_self" title="SCMFSA_2:def.5">Def5</a></i>;<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"><font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c14">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c9">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">F</font></span>)</span> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Maroon" title="c15">q</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E13:72"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="scmfsa_1.html#T22" title="SCMFSA_1:th.22">SCMFSA_1:22</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c14">f</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E16:72"><i><font color="Green" title="E58">A9</font></i></a>, <a class="txt" href="scmfsa_2.html#E19:72"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="scmfsa_1.html#T30" title="SCMFSA_1:th.30">SCMFSA_1:30</a></i>
;<br/>


</div>
