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

<b>thus </b><a NAME="E1:121_1_1"/>
 <a href="scmfsa_2.html#K1">SCM+FSA</a>  is <a href="amistd_2.html#V2">homogeneous</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">J</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D4">AMISTD_2:def 4</a><br/>

<b>assume </b><a NAME="E1:121_1_1_1"/><i><font color="Green">E53</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font>
 ;<br/>

<a NAME="E2:121_1_1_1"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_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> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_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"><b>hence </b><a NAME="E2:121_1_1_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_1_1_2"/><i><font color="Green">E102</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_2_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_2_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_2_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_2_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_2_1_1_2"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_2_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_2_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_2"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_3"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_1_1_3"/><i><font color="Green">E105</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_3_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_3_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_3_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_3_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_3_1_1_2"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_3_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_3_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_4"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_4"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_1_1_4"/><i><font color="Green">E166</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_4_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_4_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_4_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_4_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_4_1_1_2"/><i><font color="Green">E167</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_4_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_4_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_4_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_4"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_5"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_5"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_1_1_5"/><i><font color="Green">E169</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_5_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_5_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_5_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_5_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_5_1_1_2"/><i><font color="Green">E170</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_5_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_5_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_5_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_5"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_6"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_6"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_6"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_1_1_6"/><i><font color="Green">E172</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_6_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_6_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_6_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_6_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_6_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_6_1_1_2"/><i><font color="Green">E173</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_6_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_6_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_6_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_6"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_7"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_7"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">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="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_7"/><i><font color="Green">E184</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_1_1_7"/><i><font color="Green">E185</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_7_1_1"/>
( <font color="Maroon">J</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">i2</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i2</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_7_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_7_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_7_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_7_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_7_1_1_2"/>
 ex <font color="Olive">i2</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_7_1_1_2"/><i><font color="Green">E200</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_7_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_7_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_7_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_7"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_8"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_8"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_8"/><i><font color="Green">E201</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_1_1_8"/><i><font color="Green">E202</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_8_1_1"/>
( <font color="Maroon">J</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">i2</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">d1</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i2</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_8_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_8_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_8_1_1_2"/>
 ex <font color="Olive">i2</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">d1</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_8_1_1_2"/><i><font color="Green">E203</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_8_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_8_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_8_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_8"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_9"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_9"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_9"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_1_1_9"/><i><font color="Green">E205</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 8
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_9_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_9_1_1"/>
( <font color="Maroon">J</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">i2</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">d1</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i2</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_9_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_9_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_9_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_9_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_9_1_1_2"/>
 ex <font color="Olive">i2</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">d1</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i2</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_9_1_1_2"/><i><font color="Green">E206</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_9_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_9_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_9_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_9"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_10"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_10"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_10"/><i><font color="Green">E207</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font>
 ;<br/><a NAME="E4:121_1_1_1_1_10"/><i><font color="Green">E208</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 9
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_10_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_10_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_10_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_10_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_10_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_10_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_10_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_10_1_1_2"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f1</font>,<font color="Maroon">d1</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 3
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d2</font>,<font color="Maroon">f1</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_10_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_10_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_10_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_10"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_11"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_11"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_11"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_1_1_11"/><i><font color="Green">E215</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 10
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_11_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_11_1_1"/>
( <font color="Maroon">J</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="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_11_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_11_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_11_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_11_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_11_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">d2</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_11_1_1_2"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font>,<font color="Maroon">d1</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 3
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d2</font>,<font color="Maroon">f1</font>,<font color="Maroon">d1</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_11_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_11_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_11_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_11"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_12"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_12"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_12"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E4:121_1_1_1_1_12"/><i><font color="Green">E218</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 11
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_12_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_12_1_1"/>
( <font color="Maroon">J</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> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_12_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_12_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_12_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_12_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_12_1_1_2"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_12_1_1_2"/><i><font color="Green">E219</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f1</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">f1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_12_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_12_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_12_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_12"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_13"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_13"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_13"/><i><font color="Green">E220</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E4:121_1_1_1_1_13"/><i><font color="Green">E221</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 12
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_1_1_13_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_1_1_13_1_1"/>
( <font color="Maroon">J</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> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_13_1_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_13_1_1_1"/>
<font color="Maroon">J</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"><b>hence </b><a NAME="E2:121_1_1_1_1_13_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T53">SCMFSA_2:53</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_13_1_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_13_1_1_2"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f1</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_1_1_13_1_1_2"/><i><font color="Green">E222</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">d1</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">f1</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_1_1_13_1_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_1_1_13_1_1_3"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:121_1_1_1_1_13_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa_2.html#T42">SCMFSA_2:42</a>, <a class="ref" href="scmfsa_2.html#T43">SCMFSA_2:43</a>, <a class="ref" href="scmfsa_2.html#T44">SCMFSA_2:44</a>, <a class="ref" href="scmfsa_2.html#T45">SCMFSA_2:45</a>, <a class="ref" href="scmfsa_2.html#T46">SCMFSA_2:46</a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T48">SCMFSA_2:48</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T50">SCMFSA_2:50</a>, <a class="ref" href="scmfsa_2.html#T51">SCMFSA_2:51</a>, <a class="ref" href="scmfsa_2.html#T52">SCMFSA_2:52</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:121_1_1_1_1_13"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:121_1_1"/>
 <a href="scmfsa_2.html#K1">SCM+FSA</a>  is <a href="amistd_2.html#V5">with_explicit_jumps</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="121_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D8">AMISTD_2:def 8</a><br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D6">AMISTD_2:def 6</a><br/>



<b>assume </b><a NAME="E1:121_1_1_2"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_2_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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_1"/><i><font color="Green">E224</font></i>: 
<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="E2:121_1_1_2_1_1"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E3:121_1_1_2_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_2"/><i><font color="Green">E225</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_2_1_2"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_2"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_3"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_3"/><i><font color="Green">E226</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_2_1_3"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_3"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_4"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_4"/><i><font color="Green">E227</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_2_1_4"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_4"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_5"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_5"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_2_1_5"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_5"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_6"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_6"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_6"/><i><font color="Green">E229</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_2_1_6"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_6"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_7"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_7"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">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="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_7"/><i><font color="Green">E230</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_2_1_7"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</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/>;<br/><a NAME="E5:121_1_1_2_1_7"/><b>then </b><i><font color="Green">E231</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>take </b>
1
;<br/><a NAME="E6:121_1_1_2_1_7"/><i><font color="Green">E232</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:121_1_1_2_1_7"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><b>hence </b><a NAME="E8:121_1_1_2_1_7"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>thus </b><a NAME="E9:121_1_1_2_1_7"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa10.html#T3" target="_self">Th3</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_8"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_8"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_8"/><i><font color="Green">E233</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_2_1_8"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</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="txt" href="scmfsa10.html#E18"><i><font color="Green">Lemma82</font></i></a></i>;<br/><a NAME="E5:121_1_1_2_1_8"/><b>then </b><i><font color="Green">E234</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>take </b>
1
;<br/><a NAME="E6:121_1_1_2_1_8"/><i><font color="Green">E235</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:121_1_1_2_1_8"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 <b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><b>hence </b><a NAME="E8:121_1_1_2_1_8"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>thus </b><a NAME="E9:121_1_1_2_1_8"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa10.html#T4" target="_self">Th4</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_9"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_9"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_9"/><i><font color="Green">E236</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_2_1_9"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</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="txt" href="scmfsa10.html#E19"><i><font color="Green">Lemma84</font></i></a></i>;<br/><a NAME="E5:121_1_1_2_1_9"/><b>then </b><i><font color="Green">E237</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>take </b>
1
;<br/><a NAME="E6:121_1_1_2_1_9"/><i><font color="Green">E238</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:121_1_1_2_1_9"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 <b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><b>hence </b><a NAME="E8:121_1_1_2_1_9"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>thus </b><a NAME="E9:121_1_1_2_1_9"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa10.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_10"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_10"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_10"/><i><font color="Green">E239</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font>
 ;<br/><a NAME="E4:121_1_1_2_1_10"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_10"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_11"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_11"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_11"/><i><font color="Green">E240</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_2_1_11"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_11"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_12"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_12"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_12"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E4:121_1_1_2_1_12"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_12"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_2_1_13"><b>suppose </b></a><a NAME="E1:121_1_1_2_1_13"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_2_1_13"/><i><font color="Green">E242</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E4:121_1_1_2_1_13"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:121_1_1_2_1_13"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D9">AMISTD_2:def 9</a><br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D7">AMISTD_2:def 7</a><br/>



<b>given </b><font color="Maroon">k</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E3:121_1_1"/><i><font color="Green">E243</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>and </b><br/><a NAME="E4:121_1_1"/><i><font color="Green">E244</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E5:121_1_1"/><i><font color="Green">E245</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:121_1_1_3"/>
( <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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Olive">i1</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T120">SCMFSA_2:120</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_1"><b>suppose </b></a><a NAME="E1:121_1_1_3_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="E2:121_1_1_3_1"/><b>then </b>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a>, <a class="ref" href="scmfsa_2.html#T123">SCMFSA_2:123</a></i>;<br/><b>hence </b><a NAME="E3:121_1_1_3_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_2"><b>suppose </b></a><a NAME="E1:121_1_1_3_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_2"/><i><font color="Green">E246</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_3_2"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_2"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_3"><b>suppose </b></a><a NAME="E1:121_1_1_3_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_3"/><i><font color="Green">E247</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_3_3"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_3"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_3"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_4"><b>suppose </b></a><a NAME="E1:121_1_1_3_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_4"/><i><font color="Green">E248</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_3_4"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_4"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_4"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , <a class="ref" href="scmfsa10.html#T1" target="_self">Th1</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_5"><b>suppose </b></a><a NAME="E1:121_1_1_3_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_5"/><i><font color="Green">E249</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_3_5"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_5"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_5"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_6"><b>suppose </b></a><a NAME="E1:121_1_1_3_6"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_6"/><i><font color="Green">E250</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12">Divide</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_3_6"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_6"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_6"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_7"><b>suppose </b></a><a NAME="E1:121_1_1_3_7"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">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="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_7"/><i><font color="Green">E251</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_3_7"/><i><font color="Green">E252</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_7"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E6:121_1_1_3_7"/><b>then </b><i><font color="Green">E253</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E7:121_1_1_3_7"/>
 <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</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="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><b>hence </b><a NAME="E8:121_1_1_3_7"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_8"><b>suppose </b></a><a NAME="E1:121_1_1_3_8"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Olive">i1</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_8"/><i><font color="Green">E254</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_3_8"/><i><font color="Green">E255</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_8"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E6:121_1_1_3_8"/><b>then </b><i><font color="Green">E256</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, , <a class="ref" href="scmfsa10.html#T5" target="_self">Th5</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E7:121_1_1_3_8"/>
 <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</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="scmfsa10.html#T27" target="_self">Th27</a>, <a class="txt" href="scmfsa10.html#E18"><i><font color="Green">Lemma82</font></i></a></i>;<br/><b>hence </b><a NAME="E8:121_1_1_3_8"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_9"><b>suppose </b></a><a NAME="E1:121_1_1_3_9"/>
 ex <font color="Olive">i1</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K15">&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="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">i1</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_9"/><i><font color="Green">E257</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:121_1_1_3_9"/><i><font color="Green">E258</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_9"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, </i>;<br/><a NAME="E6:121_1_1_3_9"/><b>then </b><i><font color="Green">E259</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T25" target="_self">Th25</a>, <a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, <a class="ref" href="scmfsa10.html#T28" target="_self">Th28</a>, , <a class="ref" href="scmfsa10.html#T7" target="_self">Th7</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E7:121_1_1_3_9"/>
 <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</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="scmfsa10.html#T27" target="_self">Th27</a>, <a class="txt" href="scmfsa10.html#E19"><i><font color="Green">Lemma84</font></i></a></i>;<br/><b>hence </b><a NAME="E8:121_1_1_3_9"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T29" target="_self">Th29</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_10"><b>suppose </b></a><a NAME="E1:121_1_1_3_10"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Olive">f</font>,<font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_10"/><i><font color="Green">E260</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font>
 ;<br/><a NAME="E4:121_1_1_3_10"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_10"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_10"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , , <a class="ref" href="scmfsa10.html#T8" target="_self">Th8</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_11"><b>suppose </b></a><a NAME="E1:121_1_1_3_11"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">b</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_11"/><i><font color="Green">E261</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E4:121_1_1_3_11"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">f</font>,<font color="Maroon">a</font></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_11"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_11"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_12"><b>suppose </b></a><a NAME="E1:121_1_1_3_12"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Olive">f</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_12"/><i><font color="Green">E262</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E4:121_1_1_3_12"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_12"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_12"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="121_1_1_3_13"><b>suppose </b></a><a NAME="E1:121_1_1_3_13"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">f</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:121_1_1_3_13"/><i><font color="Green">E263</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E4:121_1_1_3_13"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T24" target="_self">Th24</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, </i>;<br/><a NAME="E5:121_1_1_3_13"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:121_1_1_3_13"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa10.html#T26" target="_self">Th26</a>, <a class="ref" href="scmfsa10.html#T27" target="_self">Th27</a>, , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
