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

<b>let </b><font color="Maroon" title="c1">il</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c3">N</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:103_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c5">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:103_1_1"/><i><font color="Green" title="E90">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Y</font> &amp; <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E5:103_1_1"/><i><font color="Green" title="E91">A2</font></i>: 
<font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c6">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:103_1_1_1"/>
( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">i1</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120" title="SCMFSA_2:th.120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_1"><b>suppose </b></a><a NAME="E1:103_1_1_1_1"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:103_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">x</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"><font color="Maroon" title="c1">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="scmfsa10.html#T68" target="_self" title="SCMFSA10:th.68">Th68</a>, <a class="ref" href="ami_3.html#T71" title="AMI_3:th.71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T123" title="SCMFSA_2:th.123">SCMFSA_2:123</a></i>;<br/><a NAME="E3:103_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:103_1_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_2"><b>suppose </b></a><a NAME="E1:103_1_1_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_2"/><i><font color="Green" title="E92">A3</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Maroon" title="c8">b</font>
 ;<br/><a NAME="E4:103_1_1_1_2"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">:=</a> <font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_2"><i><font color="Green" title="E92">A3</font></i></a>, <a class="ref" href="scmfsa10.html#T69" target="_self" title="SCMFSA10:th.69">Th69</a></i>;<br/><a NAME="E5:103_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_3"><b>suppose </b></a><a NAME="E1:103_1_1_1_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_3"/><i><font color="Green" title="E92">A4</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>
 ;<br/><a NAME="E4:103_1_1_1_3"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_3"><i><font color="Green" title="E92">A4</font></i></a>, <a class="ref" href="scmfsa10.html#T70" target="_self" title="SCMFSA10:th.70">Th70</a></i>;<br/><a NAME="E5:103_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_3"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_4"><b>suppose </b></a><a NAME="E1:103_1_1_1_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_4"/><i><font color="Green" title="E92">A5</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>
 ;<br/><a NAME="E4:103_1_1_1_4"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">SubFrom</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_4"><i><font color="Green" title="E92">A5</font></i></a>, <a class="ref" href="scmfsa10.html#T71" target="_self" title="SCMFSA10:th.71">Th71</a></i>;<br/><a NAME="E5:103_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_4"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_5"><b>suppose </b></a><a NAME="E1:103_1_1_1_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_5"/><i><font color="Green" title="E92">A6</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>
 ;<br/><a NAME="E4:103_1_1_1_5"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">MultBy</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_5"><i><font color="Green" title="E92">A6</font></i></a>, <a class="ref" href="scmfsa10.html#T72" target="_self" title="SCMFSA10:th.72">Th72</a></i>;<br/><a NAME="E5:103_1_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_5"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_6"><b>suppose </b></a><a NAME="E1:103_1_1_1_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_6"/><i><font color="Green" title="E92">A7</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>
 ;<br/><a NAME="E4:103_1_1_1_6"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">Divide</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_6"><i><font color="Green" title="E92">A7</font></i></a>, <a class="ref" href="scmfsa10.html#T73" target="_self" title="SCMFSA10:th.73">Th73</a></i>;<br/><a NAME="E5:103_1_1_1_6"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_6"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_7"><b>suppose </b></a><a NAME="E1:103_1_1_1_7"/>
 ex <font color="Olive" title="b1">i1</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Olive" title="b1">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">i1</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_7"/><i><font color="Green" title="E92">A8</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c7">i1</font>
 ;<br/><a NAME="E4:103_1_1_1_7"/>
<font color="Maroon" title="c4">x</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"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c6">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_7"><i><font color="Green" title="E92">A8</font></i></a>, <a class="ref" href="scmfsa10.html#T74" target="_self" title="SCMFSA10:th.74">Th74</a></i>;<br/><a NAME="E5:103_1_1_1_7"/><b>then </b>
<font color="Maroon" title="c4">x</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"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1_1_7"><i><font color="Green" title="E92">A8</font></i></a>, <a class="ref" href="scmfsa10.html#T75" target="_self" title="SCMFSA10:th.75">Th75</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_7"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_8"><b>suppose </b></a><a NAME="E1:103_1_1_1_8"/>
 ex <font color="Olive" title="b1">i1</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Olive" title="b1">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">i1</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c8">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_8"/><i><font color="Green" title="E92">A9</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c7">i1</font>
 ;<br/><a NAME="E4:103_1_1_1_8"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_8"><i><font color="Green" title="E92">A9</font></i></a>, <a class="ref" href="scmfsa10.html#T77" target="_self" title="SCMFSA10:th.77">Th77</a></i>;<br/><a NAME="E5:103_1_1_1_8"/><b>then </b><i><font color="Green" title="E93">A10</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font> &amp; not <font color="Maroon" title="c4">x</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"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:103_1_1_1_8"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c7">i1</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1_1_8"><i><font color="Green" title="E92">A9</font></i></a>, <a class="ref" href="scmfsa10.html#T76" target="_self" title="SCMFSA10:th.76">Th76</a></i>;<br/><a NAME="E7:103_1_1_1_8"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i1</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font> )
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:103_1_1_1_8"><i><font color="Green" title="E93">A10</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E8:103_1_1_1_8"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:103_1_1_1_8"><i><font color="Green" title="E93">A10</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_9"><b>suppose </b></a><a NAME="E1:103_1_1_1_9"/>
 ex <font color="Olive" title="b1">i1</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  ex <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Olive" title="b1">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">i1</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c8">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_9"/><i><font color="Green" title="E92">A11</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Maroon" title="c7">i1</font>
 ;<br/><a NAME="E4:103_1_1_1_9"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_9"><i><font color="Green" title="E92">A11</font></i></a>, <a class="ref" href="scmfsa10.html#T79" target="_self" title="SCMFSA10:th.79">Th79</a></i>;<br/><a NAME="E5:103_1_1_1_9"/><b>then </b><i><font color="Green" title="E93">A12</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font> &amp; not <font color="Maroon" title="c4">x</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"><font color="Maroon" title="c7">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:103_1_1_1_9"/>
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c1">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c7">i1</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1_1_9"><i><font color="Green" title="E92">A11</font></i></a>, <a class="ref" href="scmfsa10.html#T78" target="_self" title="SCMFSA10:th.78">Th78</a></i>;<br/><a NAME="E7:103_1_1_1_9"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i1</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font> )
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:103_1_1_1_9"><i><font color="Green" title="E93">A12</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E8:103_1_1_1_9"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E5:103_1_1_1_9"><i><font color="Green" title="E93">A12</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_10"><b>suppose </b></a><a NAME="E1:103_1_1_1_10"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c9">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_10"/><i><font color="Green" title="E92">A13</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">a</font>
 ;<br/><a NAME="E4:103_1_1_1_10"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">b</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">a</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_10"><i><font color="Green" title="E92">A13</font></i></a>, <a class="ref" href="scmfsa10.html#T80" target="_self" title="SCMFSA10:th.80">Th80</a></i>;<br/><a NAME="E5:103_1_1_1_10"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_10"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_11"><b>suppose </b></a><a NAME="E1:103_1_1_1_11"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Olive" title="b2">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c9">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_11"/><i><font color="Green" title="E92">A14</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b</font>
 ;<br/><a NAME="E4:103_1_1_1_11"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=</a> <font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_11"><i><font color="Green" title="E92">A14</font></i></a>, <a class="ref" href="scmfsa10.html#T81" target="_self" title="SCMFSA10:th.81">Th81</a></i>;<br/><a NAME="E5:103_1_1_1_11"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_11"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_12"><b>suppose </b></a><a NAME="E1:103_1_1_1_12"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Olive" title="b2">f</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c8">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_12"/><i><font color="Green" title="E92">A15</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c8">f</font>
 ;<br/><a NAME="E4:103_1_1_1_12"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">a</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">:=len</a> <font color="Maroon" title="c8">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_12"><i><font color="Green" title="E92">A15</font></i></a>, <a class="ref" href="scmfsa10.html#T82" target="_self" title="SCMFSA10:th.82">Th82</a></i>;<br/><a NAME="E5:103_1_1_1_12"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_12"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_1_1_13"><b>suppose </b></a><a NAME="E1:103_1_1_1_13"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being   <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c8">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:103_1_1_1_13"/><i><font color="Green" title="E92">A16</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c7">a</font>
 ;<br/><a NAME="E4:103_1_1_1_13"/>
<font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c7">a</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa10.html#E3:103_1_1"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="scmfsa10.html#E5:103_1_1"><i><font color="Green" title="E91">A2</font></i></a>, <a class="txt" href="scmfsa10.html#E3:103_1_1_1_13"><i><font color="Green" title="E92">A16</font></i></a>, <a class="ref" href="scmfsa10.html#T83" target="_self" title="SCMFSA10:th.83">Th83</a></i>;<br/><a NAME="E5:103_1_1_1_13"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:103_1_1_1_13"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">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="E2:103_1"/><i><font color="Green" title="E90">A17</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:103_1_2"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">il</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font> )
 </span><b>by </b><i><a class="txt" href="scmfsa10.html#E2:103_1"><i><font color="Green" title="E90">A17</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="103_1_2_1"><b>suppose </b></a><a NAME="E1:103_1_2_1"/><i><font color="Green" title="E91">A18</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">il</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c5">i</font> =  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><a NAME="E2:103_1_2_1"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></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"><font color="Maroon" title="c1">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T68" target="_self" title="SCMFSA10:th.68">Th68</a></i>;<br/><a NAME="E3:103_1_2_1"/><b>then </b>
( <font color="Maroon" title="c4">x</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"><font color="Maroon" title="c1">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">il</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span>  )
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:103_1_2_1"><i><font color="Green" title="E91">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:103_1_2_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_1_2_2"><b>suppose </b></a><a NAME="E1:103_1_2_2"/><i><font color="Green" title="E91">A19</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font>
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ;<br/><b>set </b><font color="Maroon" title="c7">i</font> =  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>;<br/><a NAME="E3:103_1_2_2"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span>)</span>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">AddTo</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span>)</span></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">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T70" target="_self" title="SCMFSA10:th.70">Th70</a></i>;<br/><a NAME="E4:103_1_2_2"/><b>then </b>
( <font color="Maroon" title="c4">x</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"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span>  )
 <b>by </b><i><a class="txt" href="scmfsa10.html#E1:103_1_2_2"><i><font color="Green" title="E91">A19</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:103_1_2_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span> 
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E2:103"/><b>then </b>
 <a href="tarski.html#K3" title="TARSKI:func.3">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" title="AMISTD_1:func.1">NIC</a> <font color="Olive" title="b1">I</font>,<font color="Maroon" title="c1">il</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  : verum </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E3:103"/>
 <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> <font color="Maroon" title="c1">il</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">il</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">Next</a> <font color="Maroon" title="c1">il</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>


</div>
