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

<b>thus </b><a NAME="E1:70_1_1"/>
 <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  is <a href="ami_1.html#V10">realistic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:70_1_1_1"/>
the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T13">SCMFSA_1:13</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D21">AMI_1:def 21</a><br/>


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

<b>thus </b><a NAME="E2:70_1_1"/>
 <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  is <a href="ami_1.html#V5">IC-Ins-separated</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:70_1_1_2"/>
 <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> 
 
<b>by </b><i>, <a class="ref" href="scmfsa_1.html#T9">SCMFSA_1:9</a></i>;<br/>
<b>hence </b><a NAME="E2:70_1_1_2"/>
 <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  is <a href="ami_1.html#V5">IC-Ins-separated</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>;<br/>


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

<b>thus </b><a NAME="E3:70_1_1"/>
 <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  is <a href="ami_1.html#V6">data-oriented</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_3"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">A</font> =  <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="ami_1.html#D12">AMI_1:def 12</a><br/>

<b>assume </b><a NAME="E1:70_1_1_3"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> </span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="int_1.html#NM1">Integer</a> <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<a NAME="E3:70_1_1_3"/>
<a href="scmfsa_1.html#K6">SCM+FSA-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="scmfsa_1.html#K4">SCM+FSA-Instr</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#T46">FUNCT_2:46</a></i>;<br/>
<a NAME="E4:70_1_1_3"/><b>then </b>
<a href="scmfsa_1.html#K6">SCM+FSA-OK</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K4">SCM+FSA-Instr</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:70_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T16">SCMFSA_1:16</a></i>;<br/>


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

<b>thus </b><a NAME="E4:70_1_1"/>
 <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  is <a href="ami_1.html#V8">definite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D14">AMI_1:def 14</a><br/>

<b>reconsider </b><font color="Maroon">L</font> = <font color="Maroon">l</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a>  ;<br/>
<b>thus </b><a NAME="E2:70_1_1_4"/>
 <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#T11">SCMFSA_1:11</a></i>;<br/>


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

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a><br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ;<br/>





<a NAME="E5:70_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <a href="ami_2.html#K4">SCM-Instr</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">L</font>,<span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Olive">dB</font>,<font color="Olive">fA</font>,<font color="Olive">dA</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">L</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Olive">dB</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">dA</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">fA</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">L</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">dC</font>,<font color="Olive">fB</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Olive">dC</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">fB</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="scmfsa_1.html#D4">SCMFSA_1:def 4</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">I</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="scmfsa_1.html#K4">SCM+FSA-Instr</a>  ;<br/>
<b>reconsider </b><font color="Maroon">S</font> = <font color="Maroon">s</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <a href="scmfsa_1.html#K6">SCM+FSA-OK</a>  ;<br/>
<b>reconsider </b><font color="Maroon">l'</font> = <font color="Maroon">l</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a>  ;<br/>
<a NAME="E9:70_1_1"/><i><font color="Green">E49</font></i>: 
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="scmfsa_1.html#D18">SCMFSA_1:def 18</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_1_1_5"/>
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K4">SCM-Instr</a>  or <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">J</font>,<span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Olive">dB</font>,<font color="Olive">fA</font>,<font color="Olive">dA</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">J</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Olive">dB</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">dA</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">fA</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">J</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">dC</font>,<font color="Olive">fB</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Olive">dC</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">fB</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span> </span>}</span>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_1"><b>suppose </b></a><a NAME="E1:70_1_1_5_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K4">SCM-Instr</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">I</font> = <font color="Maroon">i</font> as   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a>  <b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">S</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="ami_2.html#K3">SCM-Instr-Loc</a>  <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">I</font></span>)</span> as   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  <b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a>, <a class="ref" href="scmfsa_1.html#T18">SCMFSA_1:18</a></i>;<br/><a NAME="E4:70_1_1_5_1"/><i><font color="Green">E55</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/> <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> = 
 <a href="relset_1.html#K4">dom</a> <a href="scmfsa_1.html#K6">SCM+FSA-OK</a> 
<b>by </b><i><a class="ref" href="card_3.html#T18">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">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="scmfsa_1.html#T8">SCMFSA_1:8</a></i>
;<br/><a NAME="E6:70_1_1_5_1"/><b>then </b>
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E7:70_1_1_5_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <a href="scmfsa_1.html#K3">SCM+FSA-Instr-Loc</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T20" target="_self">Th20</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T20" target="_self">Th20</a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_2"><b>suppose </b></a><a NAME="E1:70_1_1_5_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">J</font>,<span class="p3"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Olive">dB</font>,<font color="Olive">fA</font>,<font color="Olive">dA</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">J</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Olive">dB</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">dA</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">fA</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">J</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">J</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Maroon">dB</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Maroon">dA</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Maroon">fA</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:70_1_1_5_2"/><i><font color="Green">E58</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"><font color="Maroon">J</font>,<span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">dB</font>,<font color="Maroon">fA</font>,<font color="Maroon">dA</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:70_1_1_5_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">9,10</span><a href="tarski.html#K2">}</a></span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_5_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_1_1_5_2_1_1"/>
( <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 9 or <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 10 )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_2_1_1_1"><b>suppose </b></a><a NAME="E1:70_1_1_5_2_1_1_1"/>
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><a NAME="E2:70_1_1_5_2_1_1_1"/><b>then </b>
<font color="Maroon">I</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 9
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:70_1_1_5_2_1_1_1"/><b>then </b>
 <a href="scmfsa_1.html#K5">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 9
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D5">SCMFSA_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon">i</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:70_1_1_5_2_1_1_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K13">int_addr2</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E6:70_1_1_5_2_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K14">coll_addr1</a> </span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E7:70_1_1_5_2_1_1_1"/><i><font color="Green">E91</font></i>: 
 <a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K8">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K12">int_addr1</a> </span>)</span>,<font color="Maroon">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18">IC</a> <font color="Maroon">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D17">SCMFSA_1:def 17</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K8">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K12">int_addr1</a> </span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i>, <a class="ref" href="scmfsa_1.html#T23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T28">SCMFSA_1:28</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_2_1_1_2"><b>suppose </b></a><a NAME="E1:70_1_1_5_2_1_1_2"/>
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><a NAME="E2:70_1_1_5_2_1_1_2"/><b>then </b>
<font color="Maroon">I</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 10
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:70_1_1_5_2_1_1_2"/><b>then </b>
 <a href="scmfsa_1.html#K5">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 10
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D5">SCMFSA_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon">f</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:70_1_1_5_2_1_1_2"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K13">int_addr2</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E6:70_1_1_5_2_1_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K14">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">k</font>,<span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K12">int_addr1</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E7:70_1_1_5_2_1_1_2"/><i><font color="Green">E92</font></i>: 
 <a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K14">coll_addr1</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18">IC</a> <font color="Maroon">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D17">SCMFSA_1:def 17</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K9">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K14">coll_addr1</a> </span>)</span>,<font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i>, <a class="ref" href="scmfsa_1.html#T23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T32">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="E6:70_1_1_5_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_3"><b>suppose </b></a><a NAME="E1:70_1_1_5_3"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">K</font>,<span class="p3"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">dC</font>,<font color="Olive">fB</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">K</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Olive">dC</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Olive">fB</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a>  : <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">J</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 13, <font color="Maroon">dC</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K1">SCM+FSA-Data-Loc</a> , <font color="Maroon">fB</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="scmfsa_1.html#K2">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:70_1_1_5_3"/><i><font color="Green">E135</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"><font color="Maroon">J</font>,<span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">dC</font>,<font color="Maroon">fB</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:70_1_1_5_3"/><i><font color="Green">E136</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">11,12</span><a href="tarski.html#K2">}</a></span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_5_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:70_1_1_5_3_1_1"/>
( <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 11 or <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i><a class="ref" href="scmfsa_2.html#T20" target="_self">Th20</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_3_1_1_1"><b>suppose </b></a><a NAME="E1:70_1_1_5_3_1_1_1"/>
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><a NAME="E2:70_1_1_5_3_1_1_1"/><b>then </b>
<font color="Maroon">I</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 11
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:70_1_1_5_3_1_1_1"/><b>then </b>
 <a href="scmfsa_1.html#K5">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 11
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D5">SCMFSA_1:def 5</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K7">SCM+FSA-Chg</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K8">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K15">int_addr3</a> </span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K11">.</a> <span class="p5">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K16">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_1.html#K17">Next</a> <span class="p3">(<span class="default"><a href="scmfsa_1.html#K18">IC</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#D17">SCMFSA_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K8">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K15">int_addr3</a> </span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K16">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T28">SCMFSA_1:28</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="70_1_1_5_3_1_1_2"><b>suppose </b></a><a NAME="E1:70_1_1_5_3_1_1_2"/>
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><a NAME="E2:70_1_1_5_3_1_1_2"/><b>then </b>
<font color="Maroon">I</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> 12
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:70_1_1_5_3_1_1_2"/><b>then </b>
 <a href="scmfsa_1.html#K5">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 12
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D5">SCMFSA_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon">f</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:70_1_1_5_3_1_1_2"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="scmfsa_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K15">int_addr3</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E6:70_1_1_5_3_1_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="finseq_2.html#K2">|-&gt;</a> 0
 <b>and </b><br/><a NAME="E7:70_1_1_5_3_1_1_2"/><i><font color="Green">E137</font></i>: 
 <a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K16">coll_addr2</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18">IC</a> <font color="Maroon">S</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D17">SCMFSA_1:def 17</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_1.html#K19">SCM+FSA-Exec-Res</a> <font color="Maroon">I</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font> = 
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K9">SCM+FSA-Chg</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="scmfsa_1.html#K16">coll_addr2</a> </span>)</span>,<font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i>, <a class="ref" href="scmfsa_1.html#T23">SCMFSA_1:23</a></i>
<br/>.= 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l'</font>
<b>by </b><i><a class="ref" href="scmfsa_1.html#T32">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="E6:70_1_1_5_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
