<?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">IL</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">T</font> be   <a href="ami_1.html#NM10" title="AMI_1:NM.10">InsType</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span>;<br/>





<b>set </b><font color="Maroon" title="c4">A</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">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#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> :  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">T</font> </span>}</span> ;<br/>
<a NAME="E1:29"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</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#K3" title="AMISTD_2:func.3">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#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> :  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">T</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_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="c5">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:29_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><a NAME="E2:29_1_1"/><b>then </b><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:29_1_1"/><i><font color="Green" title="E20">A2</font></i>: 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="ami_1.html#D2" title="AMI_1:def.2">AMI_1:def 2</a></i>;<br/><a NAME="E4:29_1_1"/><b>then </b>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCodes</a> <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#T23" title="RELAT_1:th.23">RELAT_1:23</a></i>;<br/><a NAME="E5:29_1_1"/><b>then </b><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c6">I</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> <b>by </b><i><a class="txt" href="amistd_2.html#E3:29_1_1"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E7:29_1_1"/><i><font color="Green" title="E22">A4</font></i>: 
 <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E33"><i><font color="Green" title="E17">Lm3</font></i></a></i>;<br/><a NAME="E8:29_1_1"/>
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <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="E9:29_1_1"/>
<font color="Maroon" title="c5">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#K3" title="AMISTD_2:func.3">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#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> :  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">T</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:29_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="amistd_2.html#E5:29_1_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="amistd_2.html#E7:29_1_1"><i><font color="Green" title="E22">A4</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">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="E2:29_1"/>
<font color="Maroon" title="c5">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#K3" title="AMISTD_2:func.3">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#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> :  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">T</font> </span>}</span> 
 ;<br/>

<a NAME="E3:29_1"/><b>then </b>
 ex <font color="Olive" title="b1">I</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">N</font></span>)</span> st <br/>( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <font color="Olive" title="b1">I</font> &amp;  <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">T</font> )
 
;<br/>
<a NAME="E4:29_1"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="amistd_2.html#E33"><i><font color="Green" title="E17">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:29_1"/>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="E2:29"/>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>


</div>
