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

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">T</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">InsType</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>set </b><font color="Maroon" title="c3">A</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> where <font color="Olive" title="b1">I</font> is   <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> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> </span>}</span> ;<br/>
<a NAME="E1:41"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> where <font color="Olive" title="b1">I</font> is   <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> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>proof </b></a><div class="add">

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:41_1_1"/>
<font color="Maroon" title="c4">a</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">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/><a NAME="E2:41_1_1"/><b>then </b><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:41_1_1"/><i><font color="Green" title="E26">A2</font></i>: 
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="E4:41_1_1"/><b>then </b><i><font color="Green" title="E27">A3</font></i>: 
 <a href="ami_1.html#K18" title="AMI_1:func.18">InsCodes</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#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T24" title="RELAT_1:th.24">RELAT_1:24</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_1"/>
( <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="amistd_2.html#E4:41_1_1"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_1"><b>suppose </b></a><a NAME="E1:41_1_1_1_1"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c5">I</font> = <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> as   <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> <b>by </b><i><a class="txt" href="amistd_2.html#E3:41_1_1"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E3:41_1_1_1_1"/><i><font color="Green" title="E29">A5</font></i>: 
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self" title="AMISTD_2:th.17">Th17</a></i>;<br/><a NAME="E4:41_1_1_1_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/><b>hence </b><a NAME="E5:41_1_1_1_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> where <font color="Olive" title="b1">I</font> is   <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> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:41_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="amistd_2.html#E1:41_1_1_1_1"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="amistd_2.html#E3:41_1_1_1_1"><i><font color="Green" title="E29">A5</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1_2"><b>suppose </b></a><a NAME="E1:41_1_1_1_2"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c5">I</font> = <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> as   <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> <b>by </b><i><a class="txt" href="amistd_2.html#E3:41_1_1"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E3:41_1_1_1_2"/><i><font color="Green" title="E29">A7</font></i>: 
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self" title="AMISTD_2:th.17">Th17</a></i>;<br/><a NAME="E4:41_1_1_1_2"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c5">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></i>;<br/><b>hence </b><a NAME="E5:41_1_1_1_2"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> where <font color="Olive" title="b1">I</font> is   <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> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:41_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="amistd_2.html#E1:41_1_1_1_2"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="amistd_2.html#E3:41_1_1_1_2"><i><font color="Green" title="E29">A7</font></i></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="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:41_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">I</font></span>)</span> where <font color="Olive" title="b1">I</font> is   <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> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> </span>}</span> 
 ;<br/>

<a NAME="E3:41_1"/><b>then </b>
 ex <font color="Olive" title="b1">I</font> being  <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> st <br/>( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">I</font> &amp;  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> )
 
;<br/>
<a NAME="E4:41_1"/><b>then </b>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self" title="AMISTD_2:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E5:41_1"/>
<font color="Maroon" title="c4">a</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">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:41"/>
 <a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/>


</div>
