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

<b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">s2</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E1:3"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<a NAME="E2:3"/>
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:3"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:3"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
;<br/>
<a NAME="E5:3"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s1</font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E6:3"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E7:3"/>
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font>
 
<b>by </b><i>, <a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E8:3"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<i><font color="Green">E38</font></i>:  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/>
<a NAME="E10:3"/><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E11:3"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E12:3"/><i><font color="Green">E41</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E13:3"/><i><font color="Green">E42</font></i>: 
<a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E14:3"/><i><font color="Green">E43</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 11 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T35">SCMFSA_2:35</a></i>;<br/>
<a NAME="E15:3"/><i><font color="Green">E44</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 11 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E16:3"/><i><font color="Green">E45</font></i>: 
(  not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 9 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 <a href="nat_1.html#K1">+</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 10 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 12 )
 </span><b>by </b><i>, , , <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_1"><b>suppose </b></a><a NAME="E1:3_2_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="xxreal_0.html#R1">&lt;=</a> 8
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">I</font> = <font color="Maroon">l</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="scmfsa_2.html#T34">SCMFSA_2:34</a></i>;<br/><b>reconsider </b><font color="Maroon">S1</font> = <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a>  <a href="cat_3.html#K1">--&gt;</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">S2</font> = <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a>  <a href="cat_3.html#K1">--&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_2.html#T73">SCMFSA_2:73</a></i>;<br/><a NAME="E4:3_2_1"/><i><font color="Green">E48</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a>  <a href="cat_3.html#K1">--&gt;</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a>, <a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E5:3_2_1"/>
not  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#T48">AMI_1:48</a>, <a class="ref" href="ami_3.html#D1">AMI_3:def 1</a></i>;<br/><a NAME="E6:3_2_1"/><b>then </b>
 <a href="ami_2.html#K3">SCM-Instr-Loc</a>  <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><a NAME="E7:3_2_1"/><b>then </b>
 <a href="ami_2.html#K3">SCM-Instr-Loc</a>  <a href="xboole_0.html#R1">misses</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="ami_5.html#T33">AMI_5:33</a>, <a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/><a NAME="E8:3_2_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a>  <a href="cat_3.html#K1">--&gt;</a> <font color="Maroon">I</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="relat_1.html#T95">RELAT_1:95</a></i>;<br/><a NAME="E9:3_2_1"/><i><font color="Green">E50</font></i>: 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T23">AMI_5:23</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E10:3_2_1"/>
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="tarski.html#R1">c=</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_1.html#D1">SCMFSA_1:def 1</a>, <a class="ref" href="scmfsa_2.html#D2">SCMFSA_2:def 2</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E11:3_2_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="ami_3.html#T4">AMI_3:4</a>, <a class="ref" href="scmfsa_2.html#T7">SCMFSA_2:7</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/><i><font color="Green">E52</font></i>: <font color="Maroon">S1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T22">FUNCT_4:22</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, , <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="relat_1.html#T103">RELAT_1:103</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="funct_4.html#T22">FUNCT_4:22</a></i>
<br/>.= 
<font color="Maroon">S2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
;<br/><a NAME="E13:3_2_1"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a>  <a href="xboole_0.html#R1">misses</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</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#D2">SCMFSA_1:def 2</a>, <a class="ref" href="scmfsa_2.html#D3">SCMFSA_2:def 3</a>, <a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E14:3_2_1"/><b>then </b><i><font color="Green">E53</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a>  <a href="subset_1.html#K9">/\</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E15:3_2_1"/>
not  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/><a NAME="E16:3_2_1"/><b>then </b><i><font color="Green">E54</font></i>: 
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/><a NAME="E17:3_2_1"/>
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="xboole_0.html#R1">misses</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T13">SCMFSA_2:13</a>, <a class="ref" href="scmfsa_2.html#T14">SCMFSA_2:14</a>, <a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/><a NAME="E18:3_2_1"/><b>then </b>
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="xboole_0.html#R1">misses</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/><a NAME="E19:3_2_1"/><b>then </b><i><font color="Green">E55</font></i>: 
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><i><font color="Green">E56</font></i>: <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100">RELAT_1:100</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/><a NAME="E21:3_2_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E22:3_2_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E23:3_2_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T95">RELAT_1:95</a></i>;<br/><i><font color="Green">E58</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T83">FUNCT_4:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="scmfsa_2.html#K2">Int-Locations</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T83">FUNCT_4:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="scmfsa_2.html#K2">Int-Locations</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T22">FUNCT_4:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T4">AMI_3:4</a>, <a class="ref" href="funct_4.html#T83">FUNCT_4:83</a>, <a class="ref" href="scmfsa_1.html#D1">SCMFSA_1:def 1</a>, <a class="ref" href="scmfsa_2.html#T7">SCMFSA_2:7</a>, <a class="ref" href="scmfsa_2.html#D2">SCMFSA_2:def 2</a></i>
;<br/><i><font color="Green">E59</font></i>: <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100">RELAT_1:100</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>
;<br/><a NAME="E26:3_2_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E27:3_2_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E28:3_2_1"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T95">RELAT_1:95</a></i>;<br/><i><font color="Green">E61</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T83">FUNCT_4:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="scmfsa_2.html#K2">Int-Locations</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_4.html#T83">FUNCT_4:83</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <a href="scmfsa_2.html#K2">Int-Locations</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T22">FUNCT_4:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T4">AMI_3:4</a>, <a class="ref" href="funct_4.html#T83">FUNCT_4:83</a>, <a class="ref" href="scmfsa_1.html#D1">SCMFSA_1:def 1</a>, <a class="ref" href="scmfsa_2.html#T7">SCMFSA_2:7</a>, <a class="ref" href="scmfsa_2.html#D2">SCMFSA_2:def 2</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</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">S1</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a>, <a class="ref" href="scmfsa_2.html#T75">SCMFSA_2:75</a>, <a class="ref" href="scmfsa_2.html#D1">SCMFSA_2:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</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">S1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T22">FUNCT_4:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_5.html#T58">AMI_5:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<font color="Maroon">S2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</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">S2</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="funct_4.html#T22">FUNCT_4:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</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">S2</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D1">AMI_3:def 1</a>, <a class="ref" href="scmfsa_2.html#T75">SCMFSA_2:75</a>, <a class="ref" href="scmfsa_2.html#D1">SCMFSA_2:def 1</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_2"><b>suppose </b></a><a NAME="E1:3_2_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:3_2_2"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">db</font> <a href="scmfsa_2.html#K16">:=</a> <font color="Maroon">fa</font>,<font color="Maroon">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T62">SCMFSA_2:62</a></i>;<br/><a NAME="E4:3_2_2"/>
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/><a NAME="E5:3_2_2"/><b>then </b>
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><i><font color="Green">E63</font></i>: <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E7:3_2_2"/><i><font color="Green">E64</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E8:3_2_2"/><i><font color="Green">E65</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:3_2_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_2_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:3_2_2_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:3_2_2_2"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:3_2_2_2"/><i><font color="Green">E69</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_2_2_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  )
 </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="3_2_2_2_1_1"><b>suppose </b></a><a NAME="E1:3_2_2_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><a NAME="E3:3_2_2_2_1_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:3_2_2_2_1_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_2_2_1_2"><b>suppose </b></a><a NAME="E1:3_2_2_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><a NAME="E3:3_2_2_2_1_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E10:3_2_2"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E11:3_2_2"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/><a NAME="E12:3_2_2"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E14:3_2_2"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E15:3_2_2"/><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k1</font>
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><b>consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E17:3_2_2"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E18:3_2_2"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k2</font>
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>;<br/><i><font color="Green">E82</font></i>: <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E20:3_2_2"/>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T10">SCMFSA_2:10</a></i>;<br/><a NAME="E21:3_2_2"/><b>then </b>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E22:3_2_2"/><b>then </b><i><font color="Green">E83</font></i>: 
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">fa</font>
<b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E24:3_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">db</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, , , , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E25:3_2_2"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T98">SCMFSA_2:98</a></i>
;<br/><a NAME="E27:3_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E28:3_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T4" target="_self">Th4</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_3"><b>suppose </b></a><a NAME="E1:3_2_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">db</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:3_2_3"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font>,<font color="Maroon">da</font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T63">SCMFSA_2:63</a></i>;<br/><a NAME="E4:3_2_3"/>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T10">SCMFSA_2:10</a></i>;<br/><a NAME="E5:3_2_3"/><b>then </b>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><i><font color="Green">E86</font></i>: <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E7:3_2_3"/><i><font color="Green">E87</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E8:3_2_3"/><i><font color="Green">E88</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:3_2_3"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_2_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:3_2_3_2"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:3_2_3_2"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:3_2_3_2"/><i><font color="Green">E91</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_2_3_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  )
 </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="3_2_3_2_1_1"><b>suppose </b></a><a NAME="E1:3_2_3_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><a NAME="E3:3_2_3_2_1_1"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_3_2_1_2"><b>suppose </b></a><a NAME="E1:3_2_3_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><a NAME="E3:3_2_3_2_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">fa</font>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:3_2_3_2_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E10:3_2_3"/><b>then </b><i><font color="Green">E95</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E11:3_2_3"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/><a NAME="E12:3_2_3"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E14:3_2_3"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E15:3_2_3"/><i><font color="Green">E98</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">k1</font>,<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><b>consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E17:3_2_3"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E18:3_2_3"/><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">k2</font>,<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/><i><font color="Green">E101</font></i>: <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E20:3_2_3"/>
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/><a NAME="E21:3_2_3"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">db</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><i><font color="Green">E103</font></i>: <font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">db</font>
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E23:3_2_3"/>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T10">SCMFSA_2:10</a></i>;<br/><a NAME="E24:3_2_3"/><b>then </b>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E25:3_2_3"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">fa</font>
<b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E27:3_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, , , , <a class="ref" href="scmfsa_3.html#T4" target="_self">Th4</a>, <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E28:3_2_3"/><b>then </b><i><font color="Green">E105</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
;<br/><a NAME="E30:3_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E31:3_2_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_4"><b>suppose </b></a><a NAME="E1:3_2_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:3_2_4"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmfsa_2.html#K18">:=len</a> <font color="Maroon">fa</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T64">SCMFSA_2:64</a></i>;<br/><a NAME="E4:3_2_4"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/><a NAME="E5:3_2_4"/><b>then </b>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><i><font color="Green">E107</font></i>: <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E7:3_2_4"/><i><font color="Green">E108</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E8:3_2_4"/><i><font color="Green">E109</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:3_2_4"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_2_4_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:3_2_4_2"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:3_2_4_2"/><b>then </b><i><font color="Green">E111</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:3_2_4_2"/><i><font color="Green">E112</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_2_4_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  )
 </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="3_2_4_2_1_1"><b>suppose </b></a><a NAME="E1:3_2_4_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><a NAME="E3:3_2_4_2_1_1"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:3_2_4_2_1_1"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_4_2_1_2"><b>suppose </b></a><a NAME="E1:3_2_4_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><a NAME="E3:3_2_4_2_1_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E10:3_2_4"/><b>then </b><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E11:3_2_4"/>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T10">SCMFSA_2:10</a></i>;<br/><a NAME="E12:3_2_4"/><b>then </b>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E13:3_2_4"/><b>then </b><i><font color="Green">E117</font></i>: 
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">fa</font>
<b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><b>then </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/><a NAME="E16:3_2_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">da</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E17:3_2_4"/><b>then </b><i><font color="Green">E118</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T100">SCMFSA_2:100</a></i>
;<br/><a NAME="E19:3_2_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E20:3_2_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_5"><b>suppose </b></a><a NAME="E1:3_2_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> , <font color="Maroon">fa</font> being    <a href="scmfsa_2.html#M2">FinSeq-Location</a> <b> such that </b><br/><a NAME="E3:3_2_5"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">fa</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">da</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T65">SCMFSA_2:65</a></i>;<br/><a NAME="E4:3_2_5"/>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T10">SCMFSA_2:10</a></i>;<br/><a NAME="E5:3_2_5"/><b>then </b>
<font color="Maroon">fa</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>then </b><i><font color="Green">E120</font></i>: <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  = 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
;<br/><a NAME="E7:3_2_5"/><i><font color="Green">E121</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E8:3_2_5"/><i><font color="Green">E122</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/><a NAME="E9:3_2_5"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_2_5_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:3_2_5_2"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E2:3_2_5_2"/><b>then </b><i><font color="Green">E124</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:3_2_5_2"/><i><font color="Green">E125</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_2_5_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a>  )
 </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="3_2_5_2_1_1"><b>suppose </b></a><a NAME="E1:3_2_5_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T11">SCMFSA_2:11</a></i>;<br/><a NAME="E3:3_2_5_2_1_1"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_2_5_2_1_2"><b>suppose </b></a><a NAME="E1:3_2_5_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as    <a href="scmfsa_2.html#M2">FinSeq-Location</a>  <b>by </b><i><a class="ref" href="scmfsa_2.html#T12">SCMFSA_2:12</a></i>;<br/><a NAME="E3:3_2_5_2_1_2"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">fa</font>
 <b>by </b><i><a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:3_2_5_2_1_2"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s1</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E10:3_2_5"/><b>then </b><i><font color="Green">E129</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><a NAME="E11:3_2_5"/>
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a>  <a href="scmfsa_2.html#K2">Int-Locations</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T9">SCMFSA_2:9</a></i>;<br/><a NAME="E12:3_2_5"/><b>then </b><i><font color="Green">E130</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R2">in</a> <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E14:3_2_5"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E15:3_2_5"/><i><font color="Green">E132</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k1</font> <a href="finseq_2.html#K2">|-&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><b>consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E17:3_2_5"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font></span>)</span>
 <b>and </b><br/><a NAME="E18:3_2_5"/><i><font color="Green">E134</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">fa</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k2</font> <a href="finseq_2.html#K2">|-&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/><font color="Maroon">s1</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">da</font>
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><a NAME="E20:3_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">fa</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="scmfsa_3.html#T1" target="_self">Th1</a>, <a class="ref" href="scmfsa_3.html#T2" target="_self">Th2</a>, , , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><a NAME="E21:3_2_5"/><b>then </b><i><font color="Green">E135</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
;<br/><a NAME="E23:3_2_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, , <a class="ref" href="ami_3.html#T24">AMI_3:24</a></i>;<br/><b>hence </b><a NAME="E24:3_2_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s1</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">l</font>,<font color="Maroon">s2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="subset_1.html#K4">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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