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

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">c</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/><b>let </b><font color="Maroon" title="c3">loc</font> be    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/><b>let </b><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>







<b>reconsider </b><font color="Maroon" title="c5">mj</font> = <font color="Maroon" title="c3">loc</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">a'</font> = <font color="Maroon" title="c1">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" target="_self" title="AMI_3:def.2">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">I</font> = <font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">S</font> = <font color="Maroon" title="c4">s</font> as   <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">i</font> = 8 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 9 <b>by </b><i><a class="ref" href="gr_cy_1.html#T10" title="GR_CY_1:th.10">GR_CY_1:10</a></i>;<br/>
<a NAME="E6:18"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c7">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">i</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">mj</font>,<font color="Maroon" title="c6">a'</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
;<br/>
<i><font color="Green" title="E13">A2</font></i>:  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c4">s</font> = 
 <a href="ami_2.html#K19" title="AMI_2:func.19">SCM-Exec-Res</a> <font color="Maroon" title="c7">I</font>,<font color="Maroon" title="c8">S</font>
<b>by </b><i><a class="ref" href="ami_2.html#D17" title="AMI_2:def.17">AMI_2:def 17</a></i>
<br/>.= 
 <a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c8">S</font>,<span class="p1">(<span class="default"><a href="ami_2.html#K17" title="AMI_2:func.17">IFGT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K16" title="AMI_2:func.16">cond_address</a> </span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p2">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K15" title="AMI_2:func.15">cjump_address</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p3">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">IC</a> <font color="Maroon" title="c8">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E6:18"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></i>
;<br/>
<b>thus </b><a NAME="E8:18"/>
( <font color="Maroon" title="c4">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c1">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>  implies <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">loc</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:18_2"/>
<font color="Maroon" title="c4">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c1">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/>

<a NAME="E2:18_2"/><b>then </b><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c8">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K16" title="AMI_2:func.16">cond_address</a> </span>)</span> <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> 
 
<b>by </b><i><a class="txt" href="ami_3.html#E6:18"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ami_2.html#T25" title="AMI_2:th.25">AMI_2:25</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_2.html#K17" title="AMI_2:func.17">IFGT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K16" title="AMI_2:func.16">cond_address</a> </span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K15" title="AMI_2:func.15">cjump_address</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">IC</a> <font color="Maroon" title="c8">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E7:18"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="ami_3.html#T4" target="_self" title="AMI_3:th.4">Th4</a>, <a class="ref" href="ami_2.html#T16" title="AMI_2:th.16">AMI_2:16</a></i>
<br/>.= 
<font color="Maroon" title="c7">I</font> <a href="ami_2.html#K15" title="AMI_2:func.15">cjump_address</a> 
<b>by </b><i><a class="txt" href="ami_3.html#E2:18_2"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="ami_2.html#D14" title="AMI_2:def.14">AMI_2:def 14</a></i>
<br/>.= 
<font color="Maroon" title="c3">loc</font>
<b>by </b><i><a class="txt" href="ami_3.html#E6:18"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ami_2.html#T25" title="AMI_2:th.25">AMI_2:25</a></i>
;<br/>


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

<b>thus </b><a NAME="E9:18"/>
( <font color="Maroon" title="c4">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c1">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>  implies <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K11" title="AMI_3:func.11">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="c4">s</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:18_3"/>
<font color="Maroon" title="c4">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c1">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/>

<a NAME="E2:18_3"/><b>then </b><i><font color="Green" title="E14">A4</font></i>: 
<font color="Maroon" title="c8">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K16" title="AMI_2:func.16">cond_address</a> </span>)</span> <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> 
 
<b>by </b><i><a class="txt" href="ami_3.html#E6:18"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="ami_2.html#T25" title="AMI_2:th.25">AMI_2:25</a></i>;<br/>
<a NAME="E3:18_3"/><i><font color="Green" title="E15">A5</font></i>: 
 ex <font color="Olive" title="b1">mj</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  st <br/>( <font color="Olive" title="b1">mj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c4">s</font> &amp;  <a href="ami_3.html#K11" title="AMI_3:func.11">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="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <font color="Olive" title="b1">mj</font> )
 
<b>by </b><i><a class="ref" href="ami_3.html#D11" target="_self" title="AMI_3:def.11">Def11</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span> = 
 <a href="ami_2.html#K17" title="AMI_2:func.17">IFGT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K16" title="AMI_2:func.16">cond_address</a> </span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c7">I</font> <a href="ami_2.html#K15" title="AMI_2:func.15">cjump_address</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">IC</a> <font color="Maroon" title="c8">S</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E7:18"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="ami_3.html#T4" target="_self" title="AMI_3:th.4">Th4</a>, <a class="ref" href="ami_2.html#T16" title="AMI_2:th.16">AMI_2:16</a></i>
<br/>.= 
 <a href="ami_3.html#K11" title="AMI_3:func.11">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="c4">s</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_3.html#E2:18_3"><i><font color="Green" title="E14">A4</font></i></a>, <a class="txt" href="ami_3.html#E3:18_3"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="ami_3.html#T4" target="_self" title="AMI_3:th.4">Th4</a>, <a class="ref" href="ami_2.html#D14" title="AMI_2:def.14">AMI_2:def 14</a></i>
;<br/>


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

<b>reconsider </b><font color="Maroon" title="c10">mn</font> = <font color="Maroon" title="c2">c</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  <b>by </b><i><a class="ref" href="ami_3.html#D2" target="_self" title="AMI_3:def.2">Def2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="ami_3.html#K10" title="AMI_3:func.10">&gt;0_goto</a> <font color="Maroon" title="c3">loc</font></span>)</span>,<font color="Maroon" title="c4">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">c</font> = 
<font color="Maroon" title="c8">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">mn</font>
<b>by </b><i><a class="txt" href="ami_3.html#E7:18"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="ami_2.html#T17" title="AMI_2:th.17">AMI_2:17</a></i>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">c</font>

;<br/>


</div>
