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

<b>thus </b><a NAME="E1:60_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is <a href="ami_1.html#V9" title="AMI_1:attr.9">realistic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:60_1_1_1"/><i><font color="Green" title="E42">A1</font></i>: 
the <a href="ami_1.html#U1" title="AMI_1:sel.1">Instruction-Counter</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a>, <a class="ref" href="scmfsa_1.html#T5" title="SCMFSA_1:th.5">SCMFSA_1:5</a></i>;<br/>
<b>assume </b><a NAME="E2:60_1_1_1"/>
the <a href="ami_1.html#U1" title="AMI_1:sel.1">Instruction-Counter</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D21" title="AMI_1:def.21">AMI_1:def 21</a><br/>

<a NAME="E3:60_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Olive" title="b1">k</font>
 
<b>by </b><i><a class="txt" href="scmfsa_2.html#E1:60_1_1_1"><i><font color="Green" title="E42">A1</font></i></a></i>;<br/>
<a NAME="E4:60_1_1_1"/><b>then </b>
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
;<br/>
<b>hence </b><a NAME="E5:60_1_1_1"/>
contradiction
 ;<br/>


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

<b>thus </b><a NAME="E2:60_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:60_1_1_2"/>
 <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a>, <a class="ref" href="scmfsa_1.html#T5" title="SCMFSA_1:th.5">SCMFSA_1:5</a>, <a class="ref" href="scmfsa_1.html#T9" title="SCMFSA_1:th.9">SCMFSA_1:9</a></i>;<br/>
<b>hence </b><a NAME="E2:60_1_1_2"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D11" title="AMI_1:def.11">AMI_1:def 11</a></i>;<br/>


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

<b>thus </b><a NAME="E3:60_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">l</font> be    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D14" title="AMI_1:def.14">AMI_1:def 14</a><br/>

<b>reconsider </b><font color="Maroon" title="c2">L</font> = <font color="Maroon" title="c1">l</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a>  ;<br/>
<b>thus </b><a NAME="E2:60_1_1_3"/>
 <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T11" title="SCMFSA_1:th.11">SCMFSA_1:11</a></i>;<br/>


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

<b>let </b><font color="Maroon" title="c1">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a><br/><b>let </b><font color="Maroon" title="c2">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c3">l</font> be    <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<a NAME="E4:60_1_1"/><i><font color="Green" title="E42">A2</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">L</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">dB</font>,<font color="Olive" title="b4">fA</font>,<font color="Olive" title="b3">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">L</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">dB</font>, <font color="Olive" title="b3">dA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">fA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">dC</font>,<font color="Olive" title="b3">fB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">dC</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">fB</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">I</font> = <font color="Maroon" title="c2">i</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K6" title="SCMFSA_1:func.6">SCM+FSA-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">S</font> = <font color="Maroon" title="c1">s</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">l'</font> = <font color="Maroon" title="c3">l</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a>  ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_4"/>
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a>  or <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">dB</font>,<font color="Olive" title="b4">fA</font>,<font color="Olive" title="b3">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">dB</font>, <font color="Olive" title="b3">dA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">fA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">dC</font>,<font color="Olive" title="b3">fB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">dC</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">fB</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  )
 </span><b>by </b><i><a class="txt" href="scmfsa_2.html#E4:60_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_1"><b>suppose </b></a><a NAME="E1:60_1_1_4_1"/>
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-Instr</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c7">I</font> = <font color="Maroon" title="c2">i</font> as   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  ;<br/><b>reconsider </b><font color="Maroon" title="c8">S</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c7">I</font></span>)</span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="ref" href="scmfsa_1.html#T18" title="SCMFSA_1:th.18">SCMFSA_1:18</a></i>;<br/><a NAME="E4:60_1_1_4_1"/><i><font color="Green" title="E43">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/> <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a> 
<b>by </b><i><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="scmfsa_1.html#T8" title="SCMFSA_1:th.8">SCMFSA_1:8</a></i>
;<br/><a NAME="E6:60_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">s</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:60_1_1_4_1"/><b>then </b><i><font color="Green" title="E44">A4</font></i>: 
<font color="Maroon" title="c3">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E4:60_1_1_4_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c7">I</font>,<font color="Maroon" title="c8">S</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T75" target="_self" title="SCMFSA_2:th.75">Th75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">SCM+FSA-Instr-Loc</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:60_1_1_4_1"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E7:60_1_1_4_1"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_2"><b>suppose </b></a><a NAME="E1:60_1_1_4_2"/>
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">dB</font>,<font color="Olive" title="b4">fA</font>,<font color="Olive" title="b3">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">dB</font>, <font color="Olive" title="b3">dA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">fA</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">J</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Maroon" title="c8">dB</font>, <font color="Maroon" title="c9">dA</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Maroon" title="c10">fA</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:60_1_1_4_2"/><i><font color="Green" title="E43">A5</font></i>: 
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">J</font>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c8">dB</font>,<font color="Maroon" title="c10">fA</font>,<font color="Maroon" title="c9">dA</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:60_1_1_4_2"/><i><font color="Green" title="E44">A6</font></i>: 
<font color="Maroon" title="c7">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_4_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_4_2_1_1"/>
( <font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 )
 </span><b>by </b><i><a class="txt" href="scmfsa_2.html#E4:60_1_1_4_2"><i><font color="Green" title="E44">A6</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_2_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_4_2_1_1_1"/>
<font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ;<br/><div class="add"><a NAME="E2:60_1_1_4_2_1_1_1"/><b>then </b>
 <a href="ami_1.html#NK18" title="AMI_1:NK.18">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:60_1_1_4_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>then consider </b><font color="Maroon" title="c11">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>, <font color="Maroon" title="c12">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:60_1_1_4_2_1_1_1"/>
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:60_1_1_4_2_1_1_1"/>
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k</font>
 <b>and </b><br/><a NAME="E6:60_1_1_4_2_1_1_1"/><i><font color="Green" title="E45">A7</font></i>: 
 <a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Maroon" title="c11">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D17" title="SCMFSA_1:def.17">SCMFSA_1:def 17</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Maroon" title="c11">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:60_1_1_4_2_1_1_1"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="scmfsa_1.html#T23" title="SCMFSA_1:th.23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T28" title="SCMFSA_1:th.28">SCMFSA_1:28</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_2_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_4_2_1_1_2"/>
<font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ;<br/><div class="add"><a NAME="E2:60_1_1_4_2_1_1_2"/><b>then </b>
 <a href="ami_1.html#NK18" title="AMI_1:NK.18">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:60_1_1_4_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>then consider </b><font color="Maroon" title="c11">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> , <font color="Maroon" title="c12">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:60_1_1_4_2_1_1_2"/>
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:60_1_1_4_2_1_1_2"/>
<font color="Maroon" title="c11">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c12">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E6:60_1_1_4_2_1_1_2"/><i><font color="Green" title="E45">A8</font></i>: 
 <a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D17" title="SCMFSA_1:def.17">SCMFSA_1:def 17</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c11">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:60_1_1_4_2_1_1_2"><i><font color="Green" title="E45">A8</font></i></a>, <a class="ref" href="scmfsa_1.html#T23" title="SCMFSA_1:th.23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T32" title="SCMFSA_1:th.32">SCMFSA_1:32</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:60_1_1_4_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D18" title="SCMFSA_1:def.18">SCMFSA_1:def 18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_3"><b>suppose </b></a><a NAME="E1:60_1_1_4_3"/>
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">dC</font>,<font color="Olive" title="b3">fB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">dC</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">fB</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">J</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Maroon" title="c8">dC</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Maroon" title="c9">fB</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:60_1_1_4_3"/><i><font color="Green" title="E43">A9</font></i>: 
<font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">J</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c8">dC</font>,<font color="Maroon" title="c9">fB</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:60_1_1_4_3"/><i><font color="Green" title="E44">A10</font></i>: 
<font color="Maroon" title="c7">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_4_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_4_3_1_1"/>
( <font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 )
 </span><b>by </b><i><a class="txt" href="scmfsa_2.html#E4:60_1_1_4_3"><i><font color="Green" title="E44">A10</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_3_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_4_3_1_1_1"/>
<font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 ;<br/><div class="add"><a NAME="E2:60_1_1_4_3_1_1_1"/><b>then </b>
 <a href="ami_1.html#NK18" title="AMI_1:NK.18">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:60_1_1_4_3"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p3">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#D17" title="SCMFSA_1:def.17">SCMFSA_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T23" title="SCMFSA_1:th.23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T28" title="SCMFSA_1:th.28">SCMFSA_1:28</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_4_3_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_4_3_1_1_2"/>
<font color="Maroon" title="c7">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ;<br/><div class="add"><a NAME="E2:60_1_1_4_3_1_1_2"/><b>then </b>
 <a href="ami_1.html#NK18" title="AMI_1:NK.18">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 <b>by </b><i><a class="txt" href="scmfsa_2.html#E3:60_1_1_4_3"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>then consider </b><font color="Maroon" title="c10">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> , <font color="Maroon" title="c11">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:60_1_1_4_3_1_1_2"/>
<font color="Maroon" title="c11">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E5:60_1_1_4_3_1_1_2"/>
<font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">k</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 <b>and </b><br/><a NAME="E6:60_1_1_4_3_1_1_2"/><i><font color="Green" title="E45">A11</font></i>: 
 <a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Maroon" title="c10">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_2.html#K18" title="AMI_2:func.18">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D17" title="SCMFSA_1:def.17">SCMFSA_1:def 17</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19" title="SCMFSA_1:func.19">SCM+FSA-Exec-Res</a> <font color="Maroon" title="c4">I</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Maroon" title="c10">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="txt" href="scmfsa_2.html#E6:60_1_1_4_3_1_1_2"><i><font color="Green" title="E45">A11</font></i></a>, <a class="ref" href="scmfsa_1.html#T23" title="SCMFSA_1:th.23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T32" title="SCMFSA_1:th.32">SCMFSA_1:32</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:60_1_1_4_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D18" title="SCMFSA_1:def.18">SCMFSA_1:def 18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
