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

<b>thus </b><a NAME="E1:126_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is <a href="amistd_2.html#V11" title="AMISTD_2:attr.11">IC-good</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D18" title="AMISTD_2:def.18">AMISTD_2:def 18</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:126_1_1_1_1"/>
( <font color="Maroon" title="c1">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"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120" title="SCMFSA_2:th.120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_1"/>
<font color="Maroon" title="c1">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"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:126_1_1_1_1_1"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="ref" href="ami_3.html#T71" title="AMI_3:th.71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T123" title="SCMFSA_2:th.123">SCMFSA_2:123</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_2"/><i><font color="Green" title="E99">A1</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Maroon" title="c3">b</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_2"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_2"><i><font color="Green" title="E99">A1</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_3"/><i><font color="Green" title="E99">A2</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_3"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_3"><i><font color="Green" title="E99">A2</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_4"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_4"/><i><font color="Green" title="E99">A3</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_4"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_4"><i><font color="Green" title="E99">A3</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_5"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_5"/><i><font color="Green" title="E99">A4</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_5"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_5"><i><font color="Green" title="E99">A4</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_6"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_6"/><i><font color="Green" title="E99">A5</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_6"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_6"><i><font color="Green" title="E99">A5</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_7"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_7"/>
 ex <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Olive" title="b1">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">i1</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_7"/><i><font color="Green" title="E99">A6</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c2">i1</font>
 ;<br/><b>let </b><font color="Maroon" title="c3">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D17" title="AMISTD_2:def.17">AMISTD_2:def 17</a><br/><b>let </b><font color="Maroon" title="c4">s1</font>, <font color="Maroon" title="c5">s2</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>assume </b><a NAME="E4:126_1_1_1_1_7"/>
<font color="Maroon" title="c5">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font> <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="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="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c4">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 ;<br/><a NAME="E5:126_1_1_1_1_7"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i1</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_7"><i><font color="Green" title="E99">A6</font></i></a>, <a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>;<br/><b>hence </b><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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c3">k</font> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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#K13" title="SCMFSA_2:func.13">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c2">i1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T95" title="SCMFSA_2:th.95">SCMFSA_2:95</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c5">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_7"><i><font color="Green" title="E99">A6</font></i></a>, <a class="ref" href="scmfsa10.html#T89" target="_self" title="SCMFSA10:th.89">Th89</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_8"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_8"/>
 ex <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Olive" title="b1">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c3">i1</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_8"/><i><font color="Green" title="E99">A7</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c3">i1</font>
 ;<br/><b>let </b><font color="Maroon" title="c4">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D17" title="AMISTD_2:def.17">AMISTD_2:def 17</a><br/><b>let </b><font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</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>assume </b><a NAME="E4:126_1_1_1_1_8"/><i><font color="Green" title="E100">A8</font></i>: 
<font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s1</font> <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="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="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 ;<br/><a NAME="E5:126_1_1_1_1_8"/><i><font color="Green" title="E101">A9</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T81" title="SCMFSA_2:th.81">SCMFSA_2:81</a></i>;<br/><a NAME="E6:126_1_1_1_1_8"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E7:126_1_1_1_1_8"/><b>then </b>
not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:126_1_1_1_1_8"><i><font color="Green" title="E101">A9</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E8:126_1_1_1_1_8"/><b>then </b><i><font color="Green" title="E102">A10</font></i>: 
<font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E4:126_1_1_1_1_8"><i><font color="Green" title="E100">A8</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1_1_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:126_1_1_1_1_8_1_1"/>
( <font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or <font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_8_1_1_1"/><i><font color="Green" title="E103">A11</font></i>: 
<font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ;<br/><div class="add"><a NAME="E2:126_1_1_1_1_8_1_1_1"/><b>then </b>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i1</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_8"><i><font color="Green" title="E99">A7</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>;<br/><b>hence </b><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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_8"><i><font color="Green" title="E102">A10</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_8_1_1_1"><i><font color="Green" title="E103">A11</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_8"><i><font color="Green" title="E99">A7</font></i></a>, <a class="ref" href="scmfsa10.html#T90" target="_self" title="SCMFSA10:th.90">Th90</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_8_1_1_2"/><i><font color="Green" title="E103">A12</font></i>: 
<font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ;<br/><div class="add"><a NAME="E2:126_1_1_1_1_8_1_1_2"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E3:126_1_1_1_1_8_1_1_2"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green" title="E104">A13</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E4:126_1_1_1_1_8"><i><font color="Green" title="E100">A8</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/><i><font color="Green" title="E105">A14</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c6">s2</font></span>)</span> = 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_8"><i><font color="Green" title="E99">A7</font></i></a>, <a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_8"><i><font color="Green" title="E102">A10</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_8_1_1_2"><i><font color="Green" title="E103">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T88" target="_self" title="SCMFSA10:th.88">Th88</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E4:126_1_1_1_1_8_1_1_2"><i><font color="Green" title="E104">A13</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>

;<br/> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span> = 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_8"><i><font color="Green" title="E99">A7</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_8_1_1_2"><i><font color="Green" title="E103">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T88" target="_self" title="SCMFSA10:th.88">Th88</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>

;<br/><b>hence </b><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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c6">s2</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>
<b>by </b><i><a class="txt" href="scmfsa10.html#E5:126_1_1_1_1_8_1_1_2"><i><font color="Green" title="E105">A14</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_8"><i><font color="Green" title="E99">A7</font></i></a>, <a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_8"><i><font color="Green" title="E102">A10</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_8_1_1_2"><i><font color="Green" title="E103">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_8"><i><font color="Green" title="E102">A10</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_8_1_1_2"><i><font color="Green" title="E103">A12</font></i></a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_8"><i><font color="Green" title="E99">A7</font></i></a>, <a class="ref" href="scmfsa10.html#T90" target="_self" title="SCMFSA10:th.90">Th90</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E10:126_1_1_1_1_8"/>
<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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_9"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_9"/>
 ex <font color="Olive" title="b1">i1</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Olive" title="b1">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c3">i1</font> being    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_9"/><i><font color="Green" title="E99">A15</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Maroon" title="c3">i1</font>
 ;<br/><b>let </b><font color="Maroon" title="c4">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D17" title="AMISTD_2:def.17">AMISTD_2:def 17</a><br/><b>let </b><font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</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>assume </b><a NAME="E4:126_1_1_1_1_9"/><i><font color="Green" title="E100">A16</font></i>: 
<font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s1</font> <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="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="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 ;<br/><a NAME="E5:126_1_1_1_1_9"/><i><font color="Green" title="E101">A17</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T81" title="SCMFSA_2:th.81">SCMFSA_2:81</a></i>;<br/><a NAME="E6:126_1_1_1_1_9"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E7:126_1_1_1_1_9"/><b>then </b>
not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:126_1_1_1_1_9"><i><font color="Green" title="E101">A17</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E8:126_1_1_1_1_9"/><b>then </b><i><font color="Green" title="E102">A18</font></i>: 
<font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s2</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E4:126_1_1_1_1_9"><i><font color="Green" title="E100">A16</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1_1_9_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:126_1_1_1_1_9_1_1"/>
( <font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or <font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_9_1_1_1"/><i><font color="Green" title="E103">A19</font></i>: 
<font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ;<br/><div class="add"><a NAME="E2:126_1_1_1_1_9_1_1_1"/><b>then </b>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i1</font>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_9"><i><font color="Green" title="E99">A15</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>;<br/><b>hence </b><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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_9"><i><font color="Green" title="E102">A18</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_9_1_1_1"><i><font color="Green" title="E103">A19</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_9"><i><font color="Green" title="E99">A15</font></i></a>, <a class="ref" href="scmfsa10.html#T91" target="_self" title="SCMFSA10:th.91">Th91</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_9_1_1_2"/><i><font color="Green" title="E103">A20</font></i>: 
<font color="Maroon" title="c5">s1</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ;<br/><div class="add"><a NAME="E2:126_1_1_1_1_9_1_1_2"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E3:126_1_1_1_1_9_1_1_2"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green" title="E104">A21</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</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> <font color="Maroon" title="c5">s1</font></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E4:126_1_1_1_1_9"><i><font color="Green" title="E100">A16</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/><i><font color="Green" title="E105">A22</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c6">s2</font></span>)</span> = 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_9"><i><font color="Green" title="E99">A15</font></i></a>, <a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_9"><i><font color="Green" title="E102">A18</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_9_1_1_2"><i><font color="Green" title="E103">A20</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T88" target="_self" title="SCMFSA10:th.88">Th88</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E4:126_1_1_1_1_9_1_1_2"><i><font color="Green" title="E104">A21</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span>

;<br/> <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span> = 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_9"><i><font color="Green" title="E99">A15</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_9_1_1_2"><i><font color="Green" title="E103">A20</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="amistd_1.html#K9" title="AMISTD_1:func.9">NextLoc</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T88" target="_self" title="SCMFSA10:th.88">Th88</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>

;<br/><b>hence </b><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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c6">s2</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>
<b>by </b><i><a class="txt" href="scmfsa10.html#E5:126_1_1_1_1_9_1_1_2"><i><font color="Green" title="E105">A22</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_9"><i><font color="Green" title="E99">A15</font></i></a>, <a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_9"><i><font color="Green" title="E102">A18</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_9_1_1_2"><i><font color="Green" title="E103">A20</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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"><font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E8:126_1_1_1_1_9"><i><font color="Green" title="E102">A18</font></i></a>, <a class="txt" href="scmfsa10.html#E1:126_1_1_1_1_9_1_1_2"><i><font color="Green" title="E103">A20</font></i></a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_9"><i><font color="Green" title="E99">A15</font></i></a>, <a class="ref" href="scmfsa10.html#T91" target="_self" title="SCMFSA10:th.91">Th91</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E10:126_1_1_1_1_9"/>
<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="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c5">s1</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</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="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<font color="Maroon" title="c6">s2</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_10"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_10"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_10"/><i><font color="Green" title="E99">A23</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">a</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_10"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_10"><i><font color="Green" title="E99">A23</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_11"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_11"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_11"/><i><font color="Green" title="E99">A24</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c3">b</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_11"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_11"><i><font color="Green" title="E99">A24</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_12"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_12"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Olive" title="b2">f</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_12"/><i><font color="Green" title="E99">A25</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c3">f</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_12"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_12"><i><font color="Green" title="E99">A25</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_13"><b>suppose </b></a><a NAME="E1:126_1_1_1_1_13"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:126_1_1_1_1_13"/><i><font color="Green" title="E99">A26</font></i>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c2">a</font>
 ;<br/><b>thus </b><a NAME="E4:126_1_1_1_1_13"/>
<font color="Maroon" title="c1">I</font> is <a href="amistd_2.html#V10" title="AMISTD_2:attr.10">IC-good</a>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:126_1_1_1_1_13"><i><font color="Green" title="E99">A26</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D20" title="AMISTD_2:def.20">AMISTD_2:def 20</a><br/><b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D19" title="AMISTD_2:def.19">AMISTD_2:def 19</a><br/>



<b>assume </b><a NAME="E2:126_1_1"/>
<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ;<br/>

<b>hence </b><a NAME="E3:126_1_1"/>
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c2">s1</font>, <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T32" title="SCMFSA6A:th.32">SCMFSA6A:32</a></i>;<br/>


</div>
