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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<i><font color="Green">E63</font></i>:  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D14">AMISTD_2:def 14</a></i>
<br/>.= 
6
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>
<a NAME="E2:74"/><i><font color="Green">E64</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D14">AMISTD_2:def 14</a></i>;<br/>
<i><font color="Green">E65</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a></i>
;<br/>
<a NAME="E4:74"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:74_3"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:74_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E3:74_3"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="ami_6.html#E7"><i><font color="Green">Lemma7</font></i></a></i>;<br/>
<a NAME="E4:74_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <span class="p4">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_6.html#T35" target="_self">Th35</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E6:74_3"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E7:74_3"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E1:74_3"><i><font color="Green">E66</font></i></a>, <a class="ref" href="amistd_2.html#D14">AMISTD_2:def 14</a></i>;<br/>
<font color="Maroon">c<sub>4</sub></font> = 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="ami_6.html#E6:74_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_6.html#T13" target="_self">Th13</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="ami_6.html#E3:74_3"><i><font color="Green">E67</font></i></a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="ami_6.html#E3:74_3"><i><font color="Green">E67</font></i></a>, <a class="txt" href="ami_6.html#E7:74_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="ami_6.html#T13" target="_self">Th13</a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E5:74"/><b>then </b>
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <span class="p2">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="ami_3.html#K8">goto</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_6.html#E2:74"><i><font color="Green">E64</font></i></a>, <a class="txt" href="ami_6.html#E3:74"><i><font color="Green">E65</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E6:74"/>
 <a href="amistd_2.html#K8">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_3.html#K8">goto</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <a href="ami_3.html#K1">SCM</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_6.html#E1:74"><i><font color="Green">E63</font></i></a>, <a class="ref" href="amistd_2.html#T16">AMISTD_2:16</a></i>;<br/>


</div>
