<?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="E1:106"/>
(  not <font color="Maroon">I</font> is   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">la</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13" target="_self">goto</a> <font color="Olive">la</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K14" target="_self">=0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K15" target="_self">&gt;0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16" target="_self">:=</a> <font color="Olive">fa</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">fa</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18" target="_self">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19" target="_self">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:106_1"/>
<font color="Maroon">I</font> is   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">J</font> = <font color="Maroon">I</font> as   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ;<br/>
<b>set </b><font color="Maroon">n</font> =  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font>;<br/>
<a NAME="E3:106_1"/><i><font color="Green">E40</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 10 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:106_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 10
 ;<br/>

<a NAME="E2:106_1_1"/><b>then </b>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 9 <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E3:106_1_1"/><b>then </b>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 10 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<b>hence </b><a NAME="E4:106_1_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 10 )
 <b>by </b><i><a class="ref" href="cqc_the1.html#T10">CQC_THE1:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:106_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 11 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E5:106_1"/><b>then </b><i><font color="Green">E41</font></i>: 
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 12 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E6:106_1"/>
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 11 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<b>hence </b><a NAME="E7:106_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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">la</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13" target="_self">goto</a> <font color="Olive">la</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K14" target="_self">=0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K15" target="_self">&gt;0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16" target="_self">:=</a> <font color="Olive">fa</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">fa</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18" target="_self">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19" target="_self">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 <b>by </b><i>, , , , , , <a class="ref" href="scmfsa_2.html#T7" target="_self">Th7</a>, , , , , , , , </i>;<br/>


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

<b>thus </b><a NAME="E2:106"/>
( ( <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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11" 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="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">la</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13" target="_self">goto</a> <font color="Olive">la</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K14" target="_self">=0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K15" target="_self">&gt;0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16" target="_self">:=</a> <font color="Olive">fa</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">fa</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18" target="_self">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19" target="_self">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> ) implies <font color="Maroon">I</font> is   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T4">SCMFSA_1:4</a></i>;<br/>


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