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

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

<b>thus </b><a NAME="E1:29"/>
(  not <font color="Maroon">I</font> is   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">loc</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:29_1"/>
<font color="Maroon">I</font> is   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1" target="_self">SCM</a> 
 ;<br/>

<a NAME="E2:29_1"/><b>then </b>
( <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><a href="ami_2.html#K1">SCM-Halt</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">Y</font>,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">a3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">Y</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  : <font color="Olive">Y</font> <a href="hidden.html#R1">=</a> 6 </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">a1</font>,<font color="Olive">b1</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> , <font color="Olive">b1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">7,8</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">T</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">c2</font>,<font color="Olive">c3</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">T</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">c2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">T</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="ami_2.html#D4">AMI_2:def 4</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:29_1"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="ami_2.html#K1">SCM-Halt</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">Y</font>,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">a3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">Y</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  : <font color="Olive">Y</font> <a href="hidden.html#R1">=</a> 6 </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">a1</font>,<font color="Olive">b1</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> , <font color="Olive">b1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">7,8</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">T</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">c2</font>,<font color="Olive">c3</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">T</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">c2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">T</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1"/>
( <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="ami_2.html#K1">SCM-Halt</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">Y</font>,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">a3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">Y</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  : <font color="Olive">Y</font> <a href="hidden.html#R1">=</a> 6 </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">a1</font>,<font color="Olive">b1</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> , <font color="Olive">b1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">7,8</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">T</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">c2</font>,<font color="Olive">c3</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">T</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">c2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">T</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  )
 </span><b>by </b><i><a class="ref" href="ami_3.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_1"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="ami_2.html#K1">SCM-Halt</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:29_1_1_1"/>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">loc</font> )
 <b>by </b><i><a class="ref" href="ami_2.html#D1">AMI_2:def 1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_2"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">Y</font>,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">a3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">Y</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a>  : <font color="Olive">Y</font> <a href="hidden.html#R1">=</a> 6 </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">Y</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Maroon">a3</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> <b> such that </b><br/><a NAME="E3:29_1_1_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">Y</font>,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">a3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> 6 )
 ;<br/><b>reconsider </b><font color="Maroon">loc</font> = <font color="Maroon">a3</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  ;<br/><a NAME="E5:29_1_1_2"/>
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Maroon">loc</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:29_1_1_2"/>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">loc</font> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_3"><b>suppose </b></a><a NAME="E1:29_1_1_3"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">a1</font>,<font color="Olive">b1</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">a1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> , <font color="Olive">b1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">7,8</span><a href="tarski.html#K2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">K</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Maroon">a1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K3">SCM-Instr-Loc</a> , <font color="Maroon">b1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:29_1_1_3"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b1</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">7,8</span><a href="tarski.html#K2">}</a></span> )
 ;<br/><b>reconsider </b><font color="Maroon">loc</font> = <font color="Maroon">a1</font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  ;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">b1</font> as    <a href="ami_3.html#M1" target="_self">Data-Location</a>  <b>by </b><i/>;<br/><a NAME="E6:29_1_1_3"/>
( <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> 8 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:29_1_1_3"/><b>then </b>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Maroon">loc</font> or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Maroon">loc</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E8:29_1_1_3"/>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">loc</font> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_4"><b>suppose </b></a><a NAME="E1:29_1_1_4"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">T</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">c2</font>,<font color="Olive">c3</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">T</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Olive">c2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : <font color="Olive">T</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">T</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 9, <font color="Maroon">c2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Maroon">c3</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:29_1_1_4"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">T</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c2</font>,<font color="Maroon">c3</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">T</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3">}</a></span> )
 ;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">c2</font>, <font color="Maroon">b</font> = <font color="Maroon">c3</font> as    <a href="ami_3.html#M1" target="_self">Data-Location</a>  <b>by </b><i/>;<br/><a NAME="E5:29_1_1_4"/>
( <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> 5 )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E6:29_1_1_4"/><b>then </b>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Maroon">b</font> or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E7:29_1_1_4"/>
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">loc</font> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:29"/>
( ( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">loc</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  ex <font color="Olive">loc</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">loc</font> ) implies <font color="Maroon">I</font> is   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  )
 <b>by </b><i><a class="ref" href="ami_2.html#T2">AMI_2:2</a></i>;<br/>


</div>
