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

<b>thus </b><a NAME="E1:106_1_1"/>
 <a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font> 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="106_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D18" target="_self" title="AMISTD_2:def.18">AMISTD_2:def 18</a><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" target="_self" 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 <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:106_1_1_1"/><i><font color="Green" title="E57">A1</font></i>: 
<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></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="E2:106_1_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></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>
 
<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="E3:106_1_1_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span> <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> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></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>
 
<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="E58">A2</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c5">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> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></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> <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> <span class="p2">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:106_1_1_1"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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>
<b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:106_1_1_1_2"/>
(  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span><b>by </b><i><a class="ref" href="amistd_1.html#T22" title="AMISTD_1:th.22">AMISTD_1:22</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_1_2_1"><b>suppose </b></a><a NAME="E1:106_1_1_1_2_1"/><i><font color="Green" title="E59">A3</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:106_1_1_1_2_1"/><b>then </b><i><font color="Green" title="E60">A4</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s1</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> <span class="p2">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span> = 
 <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="c4">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:106_1_1_1_2_1"><i><font color="Green" title="E59">A3</font></i></a>, <a class="ref" href="amistd_1.html#T38" title="AMISTD_1:th.38">AMISTD_1:38</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>,<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="c4">s1</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>

;<br/><a NAME="E4:106_1_1_1_2_1"/><b>then </b>
 <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <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="c2">I</font>,<font color="Maroon" title="c4">s1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p2">(<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></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</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="c2">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> = 
<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="c4">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="ref" href="amistd_1.html#T37" title="AMISTD_1:th.37">AMISTD_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<b>by </b><i><a class="ref" href="amistd_1.html#T33" title="AMISTD_1:th.33">AMISTD_1:33</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">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:106_1_1_1"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="amistd_1.html#T37" title="AMISTD_1:th.37">AMISTD_1:37</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="c2">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="amistd_2.html#E2:106_1_1_1_2_1"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="amistd_1.html#T38" title="AMISTD_1:th.38">AMISTD_1:38</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_1_2_2"><b>suppose </b></a><a NAME="E1:106_1_1_1_2_2"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:106_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E59">A5</font></i>: 
<font color="Maroon" title="c2">I</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 <b>by </b><i><a class="ref" href="amistd_1.html#T20" title="AMISTD_1:th.20">AMISTD_1:20</a></i>;<br/><a NAME="E3:106_1_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c2">I</font> is <a href="amistd_2.html#V9" title="AMISTD_2:attr.9">ins-loc-free</a>
 <b>by </b><i><a class="ref" href="amistd_2.html#T23" target="_self" title="AMISTD_2:th.23">Th23</a></i>;<br/><a NAME="E4:106_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E60">A6</font></i>: 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">k</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:106_1_1_1_2_2"><i><font color="Green" title="E59">A5</font></i></a>, <a class="ref" href="amistd_2.html#T29" target="_self" title="AMISTD_2:th.29">Th29</a></i>;<br/><b>thus </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="c2">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> = 
<span class="p1">(<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>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:106_1_1_1_2_2"><i><font color="Green" title="E59">A5</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</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="c2">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="amistd_2.html#E4:106_1_1_1"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="amistd_2.html#E4:106_1_1_1_2_2"><i><font color="Green" title="E60">A6</font></i></a>, <a class="ref" href="ami_1.html#D8" title="AMI_1:def.8">AMI_1:def 8</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="c2">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D20" target="_self" title="AMISTD_2:def.20">AMISTD_2:def 20</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:106_1_1_2"/>
(  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 </span><b>by </b><i><a class="ref" href="amistd_1.html#T22" title="AMISTD_1:th.22">AMISTD_1:22</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_2_1"><b>suppose </b></a><a NAME="E1:106_1_1_2_1"/><i><font color="Green" title="E57">A7</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:106_1_1_2_1"/>
the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 <b>by </b><i><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></i>;<br/><a NAME="E3:106_1_1_2_1"/><b>then </b><i><font color="Green" title="E58">A8</font></i>: 
( <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>let </b><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D19" target="_self" title="AMISTD_2:def.19">AMISTD_2:def 19</a><br/><b>assume </b><a NAME="E4:106_1_1_2_1"/><i><font color="Green" title="E59">A9</font></i>: 
<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>
 ;<br/><b>consider </b><font color="Maroon" title="c5">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>, <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span><b> such that </b><br/><a NAME="E6:106_1_1_2_1"/><i><font color="Green" title="E60">A10</font></i>: 
for <font color="Olive" title="b1">s</font> being   <a href="pralg_2.html#M1" title="PRALG_2:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span> holds  <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:106_1_1_2_1"/><i><font color="Green" title="E61">A11</font></i>: 
the <a href="ami_1.html#U5" title="AMI_1:sel.5">Execution</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Object-Kind</a> of <span class="p4">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></i>;<br/><a NAME="E8:106_1_1_2_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E9:106_1_1_2_1"/><b>then </b>
not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:106_1_1_2_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="txt" href="amistd_2.html#E3:106_1_1_2_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E10:106_1_1_2_1"/><b>then </b>
not <font color="Maroon" title="c2">I</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"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Object-Kind</a> of <span class="p4">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E11:106_1_1_2_1"/><b>then </b><i><font color="Green" title="E62">A12</font></i>: 
the <a href="ami_1.html#U5" title="AMI_1:sel.5">Execution</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">I</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E7:106_1_1_2_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><a NAME="E12:106_1_1_2_1"/><i><font color="Green" title="E63">A13</font></i>: 
<font color="Maroon" title="c2">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:106_1_1_2_1"><i><font color="Green" title="E57">A7</font></i></a>, <a class="txt" href="amistd_2.html#E3:106_1_1_2_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a>, <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="E64">A14</font></i>:  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font> = 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s1</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E11:106_1_1_2_1"><i><font color="Green" title="E62">A12</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:106_1_1_2_1"><i><font color="Green" title="E60">A10</font></i></a></i>
;<br/><i><font color="Green" title="E65">A15</font></i>:  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s2</font> = 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s2</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E11:106_1_1_2_1"><i><font color="Green" title="E62">A12</font></i></a>, <a class="txt" href="amistd_2.html#E12:106_1_1_2_1"><i><font color="Green" title="E63">A13</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon" title="c4">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:106_1_1_2_1"><i><font color="Green" title="E60">A10</font></i></a></i>
;<br/><a NAME="E15:106_1_1_2_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="ami_1.html#U4" title="AMI_1:sel.4">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/><a NAME="E16:106_1_1_2_1"/><b>then </b><i><font color="Green" title="E66">A16</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/><a NAME="E17:106_1_1_2_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_1_2_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:106_1_1_2_1_3"/><i><font color="Green" title="E67">A17</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>
 ;<br/>

<a NAME="E2:106_1_1_2_1_3"/><b>then </b>
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:106_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E68">A18</font></i>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></i>;<br/>
<i><font color="Green" title="E69">A19</font></i>: <font color="Maroon" title="c3">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s1</font>
<b>by </b><i><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></i>
<br/>.= 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">s2</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:106_1_1_2_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="ref" href="ami_1.html#T121" title="AMI_1:th.121">AMI_1:121</a></i>
<br/>.= 
<font color="Maroon" title="c4">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<b>by </b><i><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></i>
;<br/>
<a NAME="E5:106_1_1_2_1_3"/>
<font color="Maroon" title="c6">x</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"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:106_1_1_2_1_3"><i><font color="Green" title="E67">A17</font></i></a></i>;<br/>
<a NAME="E6:106_1_1_2_1_3"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E7:106_1_1_2_1_3"/><b>then </b>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></i>;<br/>
<a NAME="E8:106_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E70">A20</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:106_1_1_2_1_3"><i><font color="Green" title="E68">A18</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E9:106_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E71">A21</font></i>: 
<font color="Maroon" title="c6">x</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"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E10:106_1_1_2_1_3"/>
<font color="Maroon" title="c6">x</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"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E8:106_1_1_2_1_3"><i><font color="Green" title="E70">A20</font></i></a>, <a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E13:106_1_1_2_1"><i><font color="Green" title="E64">A14</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E14:106_1_1_2_1"><i><font color="Green" title="E65">A15</font></i></a>, <a class="txt" href="amistd_2.html#E4:106_1_1_2_1_3"><i><font color="Green" title="E69">A19</font></i></a>, <a class="txt" href="amistd_2.html#E9:106_1_1_2_1_3"><i><font color="Green" title="E71">A21</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
;<br/><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E18:106_1_1_2_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c3">s1</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s2</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <span class="p2">(<span class="default"><a href="amistd_1.html#K4" title="AMISTD_1:func.4">STC</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E16:106_1_1_2_1"><i><font color="Green" title="E66">A16</font></i></a>, <a class="ref" href="funct_1.html#T165" title="FUNCT_1:th.165">FUNCT_1:165</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2" title="FUNCT_7:def.2">FUNCT_7:def 2</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_2_2"><b>suppose </b></a><a NAME="E1:106_1_1_2_2"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:106_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c2">I</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 <b>by </b><i><a class="ref" href="amistd_1.html#T20" title="AMISTD_1:th.20">AMISTD_1:20</a></i>;<br/><b>hence </b><a NAME="E3:106_1_1_2_2"/>
<font color="Maroon" title="c2">I</font> is <a href="amistd_2.html#V12" title="AMISTD_2:attr.12">Exec-preserving</a>
 <b>by </b><i><a class="ref" href="amistd_2.html#T46" target="_self" title="AMISTD_2:th.46">Th46</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
