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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="ami_1.html#NM8">InsType</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> :  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> ;<br/>
<a NAME="E1:43"/>
<span class="p1"><a href="realset1.html#K5">{</a><span class="default">0</span><a href="realset1.html#K5">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> :  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_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">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:43_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default">0</span><a href="realset1.html#K5">}</a></span>
 ;<br/><a NAME="E2:43_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:43_1_1"/><i><font color="Green">E30</font></i>: 
the <a href="ami_1.html#U4">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="amistd_1.html#D11">AMISTD_1:def 11</a></i>;<br/><a NAME="E4:43_1_1"/><i><font color="Green">E31</font></i>: 
the <a href="ami_1.html#U3">Instruction-Codes</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">0,1</span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="amistd_1.html#D11">AMISTD_1:def 11</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="amistd_2.html#E4:43_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_1"><b>suppose </b></a><a NAME="E1:43_1_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> as   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="amistd_2.html#E3:43_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E3:43_1_1_1_1"/><i><font color="Green">E33</font></i>: 
 <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</a></i>;<br/> <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="domain_1.html#K2">`1</a> 
<b>by </b><i><a class="ref" href="ami_5.html#D1">AMI_5:def 1</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
;<br/><b>hence </b><a NAME="E5:43_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> :  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:43_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="amistd_2.html#E1:43_1_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="amistd_2.html#E3:43_1_1_1_1"><i><font color="Green">E33</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_2"><b>suppose </b></a><a NAME="E1:43_1_1_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> as   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="amistd_2.html#E3:43_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E3:43_1_1_1_2"/><i><font color="Green">E33</font></i>: 
 <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</a></i>;<br/> <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="domain_1.html#K2">`1</a> 
<b>by </b><i><a class="ref" href="ami_5.html#D1">AMI_5:def 1</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a></i>
;<br/><b>hence </b><a NAME="E5:43_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> :  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:43_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="amistd_2.html#E1:43_1_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="amistd_2.html#E3:43_1_1_1_2"><i><font color="Green">E33</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">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:43_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> :  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span> 
 ;<br/>

<a NAME="E3:43_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<a NAME="E4:43_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E5:43_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default">0</span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:43"/>
 <a href="amistd_2.html#K5" target="_self">AddressParts</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default">0</span><a href="realset1.html#K5">}</a></span>
 ;<br/>


</div>
