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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:36_1_1_1"/>
 <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> 8
 ;<br/><b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K4">SCM-Instr</a>  <b>by </b><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="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x'</font></span>)</span> as   <a href="ami_2.html#NM1">SCM-State</a> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">s1</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16">SCM-Exec-Res</a> <font color="Maroon">x'</font>,<font color="Maroon">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</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" target="_self">SCM+FSA-Instr-Loc</a> </span>)</span> as   <a href="scmfsa_1.html#NM1">SCM+FSA-State</a> <b>by </b><i/>;<br/><b>take </b><font color="Maroon">s1</font> = <font color="Maroon">s1</font>;<br/><b>take </b><font color="Maroon">x'</font> = <font color="Maroon">x'</font>;<br/><b>take </b><font color="Maroon">s'</font> = <font color="Maroon">s'</font>;<br/><b>thus </b><a NAME="E5:36_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font>
 ;<br/><b>thus </b><a NAME="E6:36_1_1_1"/>
<font color="Maroon">s'</font> <a href="hidden.html#R1">=</a> <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="finsop_1.html#K3">--&gt;</a> <font color="Maroon">x'</font></span>)</span>
 ;<br/><b>thus </b><a NAME="E7:36_1_1_1"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16">SCM-Exec-Res</a> <font color="Maroon">x'</font>,<font color="Maroon">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</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" target="_self">SCM+FSA-Instr-Loc</a> </span>)</span>
 ;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:36_1_1_2"/>
 <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><b>reconsider </b><font color="Maroon">k</font> =  <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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K13" target="_self">int_addr2</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><b>reconsider </b><font color="Maroon">i</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>take </b><font color="Maroon">s1</font> =  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K8" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span>,<font color="Maroon">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span>;<br/><b>take </b><font color="Maroon">i</font> = <font color="Maroon">i</font>;<br/><b>take </b><font color="Maroon">k</font> = <font color="Maroon">k</font>;<br/><b>thus </b><a NAME="E4:36_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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K13" target="_self">int_addr2</a> </span>)</span></span>)</span> &amp; <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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font> &amp; <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K8" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span>,<font color="Maroon">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span> )
 ;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:36_1_1_3"/>
 <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><b>reconsider </b><font color="Maroon">k</font> =  <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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K13" target="_self">int_addr2</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_1_1_3_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> or  not <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_1"><b>suppose </b></a><a NAME="E1:36_1_1_3_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:36_1_1_3_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">k</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><b>set </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span>;<br/> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">k</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/><b>then reconsider </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/><a NAME="E5:36_1_1_3_1_1"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/><a NAME="E6:36_1_1_3_1_1"/><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E7:36_1_1_3_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/><a NAME="E8:36_1_1_3_1_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E9:36_1_1_3_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><a NAME="E10:36_1_1_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K10" target="_self">.</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/><a NAME="E11:36_1_1_3_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/><b>take </b><font color="Maroon">s1</font> =  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span>;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>take </b><font color="Maroon">k</font> = <font color="Maroon">k</font>;<br/><b>thus </b><a NAME="E13:36_1_1_3_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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K13" target="_self">int_addr2</a> </span>)</span></span>)</span>
 ;<br/><b>thus </b><a NAME="E14:36_1_1_3_1_1"/>
<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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_7.html#D3">FUNCT_7:def 3</a></i>;<br/><b>thus </b><a NAME="E15:36_1_1_3_1_1"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_2"><b>suppose </b></a><a NAME="E1:36_1_1_3_1_2"/><i><font color="Green">E39</font></i>: 
not <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span></span>)</span>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">s</font> <a href="scmfsa_1.html#K11" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  ;<br/><b>take </b><font color="Maroon">s1</font> =  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span>;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>take </b><font color="Maroon">k</font> = <font color="Maroon">k</font>;<br/><b>thus </b><a NAME="E3:36_1_1_3_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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K13" target="_self">int_addr2</a> </span>)</span></span>)</span>
 ;<br/><b>thus </b><a NAME="E4:36_1_1_3_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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K12" target="_self">int_addr1</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_7.html#D3">FUNCT_7:def 3</a></i>;<br/><b>thus </b><a NAME="E5:36_1_1_3_1_2"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K14" target="_self">coll_addr1</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>thus </b><a NAME="E4:36_1_1"/>
(  <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 11 implies  ex <font color="Olive">s1</font> being  <a href="scmfsa_1.html#NM1">SCM+FSA-State</a> st <font color="Olive">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K8" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K15" target="_self">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" target="_self">.</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K16" target="_self">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span> )
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:36_1_1_4"/>
 <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><b>reconsider </b><font color="Maroon">k</font> =  <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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K15" target="_self">int_addr3</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><a NAME="E3:36_1_1_4"/>
<font color="Maroon">k</font> <a href="finsop_1.html#K1">|-&gt;</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0
 <b>by </b><i><a class="ref" href="finseq_2.html#D2">FINSEQ_2:def 2</a></i>;<br/><a NAME="E4:36_1_1_4"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="finsop_1.html#K1">|-&gt;</a> 0</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E5:36_1_1_4"/>
0 <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/><a NAME="E6:36_1_1_4"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/><a NAME="E7:36_1_1_4"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="finsop_1.html#K1">|-&gt;</a> 0</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K4">INT</a> 
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">k</font> <a href="finsop_1.html#K1">|-&gt;</a> 0 as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/><b>take </b><font color="Maroon">s1</font> =  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K16" target="_self">coll_addr2</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span>;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>take </b><font color="Maroon">k</font> = <font color="Maroon">k</font>;<br/><b>thus </b><a NAME="E9:36_1_1_4"/>
( <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" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K15" target="_self">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="finsop_1.html#K1">|-&gt;</a> 0 &amp; <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_1.html#K7" target="_self">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" target="_self">SCM+FSA-Chg</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="scmfsa_1.html#K16" target="_self">coll_addr2</a> </span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa_1.html#K17" target="_self">Next</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" target="_self">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span> )
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E6:36_1_1"/>
( not  <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 &amp; not  <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 9 &amp; not  <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 10 &amp; not  <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 11 &amp; not  <a href="scmfsa_1.html#K5" target="_self">InsCode</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> )
 ;<br/>


</div>
