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

<b>thus </b><a NAME="E1:44_1_1"/>
 <a href="amistd_1.html#K4">STC</a> <font color="Maroon">N</font> is <a href="amistd_2.html#V5" target="_self">with_explicit_jumps</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">I</font> be   <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">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D8" target="_self">AMISTD_2:def 8</a><br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D6" target="_self">AMISTD_2:def 6</a><br/>



<b>thus </b><a NAME="E1:44_1_1_1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> implies  ex <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">N</font></span>)</span> ) )
 ;<br/>


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

<b>thus </b><a NAME="E2:44_1_1"/>
 <a href="amistd_1.html#K4">STC</a> <font color="Maroon">N</font> is <a href="amistd_2.html#V6" target="_self">without_implicit_jumps</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">I</font> be   <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">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D9" target="_self">AMISTD_2:def 9</a><br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D7" target="_self">AMISTD_2:def 7</a><br/>



<a NAME="E1:44_1_1_2"/>
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">N</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="E2:44_1_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
( <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> or <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E3:44_1_1_2"/>
 <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:44_1_1_2"/>
(  ex <font color="Olive">k</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">N</font></span>)</span> ) implies <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T26">FINSEQ_1:26</a></i>;<br/>


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

<b>let </b><font color="Maroon">T</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">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D11" target="_self">AMISTD_2:def 11</a><br/>

<b>take </b>
 <a href="xboole_0.html#K1">{}</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D2" target="_self">AMISTD_2:def 2</a><br/>

<b>thus </b><a NAME="E3:44_1_1"/>
 <a href="amistd_2.html#K5" target="_self">AddressParts</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="card_3.html#T19">CARD_3:19</a></i>;<br/>


</div>
