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

<b>let </b><font color="Maroon">il</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">N</font> = <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:58_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:58_1_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E5:58_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:58_1_1_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="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">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="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5">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="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">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="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1">Data-Location</a>  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font> being   <a href="ami_3.html#M1">Data-Location</a>  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Olive">i1</font> )
 </span><b>by </b><i><a class="ref" href="ami_3.html#T69">AMI_3:69</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1"><b>suppose </b></a><a NAME="E1:58_1_1_1_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>
 ;<br/><div class="add"><a NAME="E2:58_1_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">il</font></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="ami_6.html#T4" target="_self">Th4</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a></i>;<br/><a NAME="E3:58_1_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:58_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_2"><b>suppose </b></a><a NAME="E1:58_1_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K3">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:58_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:58_1_1_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:58_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_3"><b>suppose </b></a><a NAME="E1:58_1_1_1_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_3"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:58_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="txt" href="ami_6.html#E5:58_1_1"><i><font color="Green">E47</font></i></a></i>;<br/><a NAME="E5:58_1_1_1_3"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:58_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_4"><b>suppose </b></a><a NAME="E1:58_1_1_1_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_4"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:58_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:58_1_1_1_4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:58_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_5"><b>suppose </b></a><a NAME="E1:58_1_1_1_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_5"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:58_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:58_1_1_1_5"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:58_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_6"><b>suppose </b></a><a NAME="E1:58_1_1_1_6"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="ami_3.html#M1">Data-Location</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_6"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:58_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="ami_6.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E5:58_1_1_1_6"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:58_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_7"><b>suppose </b></a><a NAME="E1:58_1_1_1_7"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_7"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:58_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:58_1_1_1_7"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:58_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_8"><b>suppose </b></a><a NAME="E1:58_1_1_1_8"/>
 ex <font color="Olive">a</font> being   <a href="ami_3.html#M1">Data-Location</a>  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_8"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:58_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:58_1_1_1_8"/><b>then </b><i><font color="Green">E125</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:58_1_1_1_8"/>
 <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E7:58_1_1_1_8"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font> )
 <b>by </b><i><a class="txt" href="ami_6.html#E7"><i><font color="Green">Lemma61</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E8:58_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_6.html#E7"><i><font color="Green">Lemma61</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_9"><b>suppose </b></a><a NAME="E1:58_1_1_1_9"/>
 ex <font color="Olive">a</font> being   <a href="ami_3.html#M1">Data-Location</a>  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:58_1_1_1_9"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="ami_3.html#K10">&gt;0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:58_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i>, , , </i>;<br/><a NAME="E5:58_1_1_1_9"/><b>then </b><i><font color="Green">E127</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:58_1_1_1_9"/>
 <a href="amistd_1.html#K1">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">il</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="ami_6.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E7:58_1_1_1_9"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font> )
 <b>by </b><i><a class="txt" href="ami_6.html#E7"><i><font color="Green">Lemma61</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E8:58_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="ami_6.html#E7"><i><font color="Green">Lemma61</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><b>assume </b><a NAME="E2:58_1"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:58_1_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">il</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font> )
 </span><b>by </b><i>, <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="58_1_2_1"><b>suppose </b></a><a NAME="E1:58_1_2_1"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">il</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">i</font> =  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> ;<br/><a NAME="E2:58_1_2_1"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">il</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="ami_6.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E3:58_1_2_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">il</font></span><a href="realset1.html#K5">}</a></span> &amp; <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">il</font></span><a href="realset1.html#K5">}</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span>  )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:58_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_2_2"><b>suppose </b></a><a NAME="E1:58_1_2_2"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">a</font> being    <a href="ami_3.html#M1">Data-Location</a> , <font color="Maroon">b</font> being    <a href="ami_3.html#M1">Data-Location</a> ;<br/><b>set </b><font color="Maroon">i</font> =  <a href="ami_3.html#K4">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><a NAME="E3:58_1_2_2"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E4:58_1_2_2"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> &amp; <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="realset1.html#K5">}</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span>  )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:58_1_2_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E2:58"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">I</font>,<font color="Maroon">il</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">I</font></span>)</span></span>)</span> where <font color="Olive">I</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  : verum </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E3:58"/>
 <a href="amistd_1.html#K3">SUCC</a> <font color="Maroon">il</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">il</font>,<span class="p2">(<span class="default"><a href="ami_3.html#K11">Next</a> <font color="Maroon">il</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/>


</div>
