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

<b>set </b><font color="Maroon">D</font> = the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>
<b>let </b><font color="Maroon">s</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="E1:19"/><i><font color="Green">E26</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 ;<br/>

<b>let </b><font color="Maroon">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>let </b><font color="Maroon">p</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>



<b>set </b><font color="Maroon">a1</font> =  <a href="scmfsa_2.html#K4">intloc</a> 1;<br/>
<b>set </b><font color="Maroon">a2</font> =  <a href="scmfsa_2.html#K4">intloc</a> 2;<br/>
<b>assume </b><a NAME="E2:19"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">f</font> <a href="scmfsa_7.html#K5">:=</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/>

<b>set </b><font color="Maroon">q</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">q0</font> = <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>;<br/>
<a NAME="E3:19"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> <a href="scmfsa_7.html#K5">:=</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_7.html#K1">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#D5">SCMFSA_7:def 5</a></i>;<br/>
<div><i><font color="Green">E31</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_1"/><i><font color="Green">E34</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:19_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T26">SCMFSA_7:26</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">k</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_7.html#D1">SCMFSA_7:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">pp</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E6:19"/><i><font color="Green">E36</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">pp</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E7:19"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> holds <br/> ex <font color="Olive">i</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> &amp; <font color="Maroon">pp</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<font color="Olive">k</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Olive">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> )
 <b>and </b><br/><a NAME="E8:19"/><i><font color="Green">E38</font></i>: 
 <a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#D4">SCMFSA_7:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">k</font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span>;<br/>
<a NAME="E9:19"/><i><font color="Green">E39</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/>
<a NAME="E11:19"/><b>then </b>
 <a href="scmfsa_7.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="scmfsa_7.html#K5">:=</a> <font color="Maroon">p</font>
 
<b>by </b><i>, <a class="ref" href="scmfsa_7.html#T31">SCMFSA_7:31</a></i>;<br/>
<a NAME="E12:19"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="scmfsa_7.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_3"/><i><font color="Green">E52</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:19_3"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T26">SCMFSA_7:26</a></i>;<br/><a NAME="E3:19_3"/>
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><a NAME="E4:19_3"/><b>then </b>
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="scmfsa_7.html#D1">SCMFSA_7:def 1</a></i>;<br/><b>hence </b><a NAME="E5:19_3"/>
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T1" target="_self">Th1</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_4"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:19_4"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T29">SCMFSA_7:29</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font></span>)</span> = 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa7b.html#T1" target="_self">Th1</a></i>
;<br/></div><b>end;</b></div>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="finseq_1.html#NM1">FinSequence</a>] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">pp</font> implies  ex <font color="Olive">pp0</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Olive">pp0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Olive">pp0</font></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">i</font> ) ) );<br/>
<a NAME="E15:19"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="xboole_0.html#K1">{}</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_5"><b>proof </b></a><div class="add">

<i><font color="Green">E58</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p3">(<span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> </span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_7.html#T13">SCMFSA_7:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/>
<b>assume </b><a NAME="E2:19_5"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">pp</font>
 ;<br/>

<div><i><font color="Green">E59</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_5_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:19_5_2"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> implies <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> )
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E3:19_5_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font>
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div>
<a NAME="E4:19_5"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E5:19_5"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:19"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E6:19_5"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E7:19_5"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E8:19_5"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E9:19_5"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E10:19_5"/><i><font color="Green">E64</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<i><font color="Green">E65</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:19"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmfsa7b.html#E3:19"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#T85">FINSEQ_1:85</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
;<br/>
<i><font color="Green">E66</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E4:19"><i><font color="Green">E31</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/>
<i><font color="Green">E67</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</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="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T2" target="_self">Th2</a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>
;<br/>
<b>take </b>
 <a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> </span>)</span>
;<br/>

<b>thus </b><a NAME="E14:19_5"/>
 <a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_5_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_5_6"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:19_5_6"/><b>then </b>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> or <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> )
 <b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><b>hence </b><a NAME="E3:19_5_6"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:19"><i><font color="Green">E26</font></i></a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E16:19_5"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p4">(<span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> </span>)</span></span>)</span></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">i</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E16:19"/><i><font color="Green">E68</font></i>: 
for <font color="Olive">r</font> being  <a href="finseq_1.html#NM1">FinSequence</a><br/> for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">r</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">r</font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">r</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:19_6"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">r</font>]
 ;<br/>

<b>assume </b><a NAME="E2:19_6"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">pp</font>
 ;<br/>

<a NAME="E3:19_6"/>
<font color="Maroon">r</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/>
<b>then consider </b><font color="Maroon">pp0</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E5:19_6"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">pp0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E6:19_6"/><i><font color="Green">E73</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">i</font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:19"><i><font color="Green">E26</font></i></a>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>set </b><font color="Maroon">r1</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/>
<a NAME="E7:19_6"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E8:19_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T6">FINSEQ_1:6</a></i>;<br/>
<a NAME="E9:19_6"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E10:19_6"/><i><font color="Green">E75</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">pp</font>
 
<b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E11:19_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">pp</font>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E3:19"><i><font color="Green">E30</font></i></a></i>;<br/>
<a NAME="E12:19_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">pp</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E13:19_6"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">pp</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>then consider </b><font color="Maroon">pr1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E15:19_6"/>
<font color="Maroon">pr1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E16:19_6"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">pp</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E77</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_1"><b>now </b></a><div class="add"><b>thus </b><font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<font color="Maroon">pp</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="txt" href="scmfsa7b.html#E3:19"><i><font color="Green">E30</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E18:19_6"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E3:19"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:19"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E19:19_6"/><b>then </b>
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#T22">SCMFSA_7:22</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">pp1</font> = <font color="Maroon">pp0</font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="scmfsa_7.html#T23">SCMFSA_7:23</a></i>;<br/>
<b>take </b>
<font color="Maroon">pp1</font>
;<br/>

<b>thus </b><a NAME="E21:19_6"/>
<font color="Maroon">pp1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E2:19"><i><font color="Green">E28</font></i></a></i>;<br/>

<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="finseq_2.html#M2">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="txt" href="scmfsa7b.html#E3:19"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:19"><i><font color="Green">E31</font></i></a>, , <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E23:19_6"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T2" target="_self">Th2</a>, , <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E24:19_6"/><i><font color="Green">E79</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font> <a href="tarski.html#R1">c=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font>
 
<b>by </b><i>, <a class="txt" href="scmfsa7b.html#E2:19"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmfsa_7.html#T19">SCMFSA_7:19</a></i>;<br/>
<i><font color="Green">E81</font></i>:  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font> = 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_7.html#T14">SCMFSA_7:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="dtconstr.html#T13">DTCONSTR:13</a></i>
;<br/>
<a NAME="E26:19_6"/><b>then </b><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<b>set </b><font color="Maroon">c1</font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">s1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c2</font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">s2</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c3</font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span>;<br/>
<a NAME="E27:19_6"/><i><font color="Green">E83</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E28:19_6"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/>
<a NAME="E29:19_6"/><i><font color="Green">E85</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E8:19"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E30:19_6"/><i><font color="Green">E86</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<div><i><font color="Green">E87</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>assume </b><a NAME="E1:19_6_3"/>
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E2:19_6_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="finseq_6.html#T15">FINSEQ_6:15</a></i>;<br/><a NAME="E3:19_6_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font>
 <b>by </b><i>, <a class="txt" href="scmfsa7b.html#E6:19"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E4:19_6_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">p</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_6.html#T15">FINSEQ_6:15</a></i>;<br/><a NAME="E5:19_6_3"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E6:19_6_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/><b>hence </b><a NAME="E7:19_6_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T5" target="_self">Th5</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E32:19_6"/><i><font color="Green">E89</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">c</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">c</font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_4"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:19_6_4"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E2:19_6_4"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/>

<a NAME="E3:19_6_4"/>
 <a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/>
<a NAME="E4:19_6_4"/><b>then </b><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E5:19_6_4"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E6:19_6_4"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E12:19"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scmfsa_7.html#T28">SCMFSA_7:28</a></i>;<br/>
<a NAME="E7:19_6_4"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E8:19_6_4"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/>
<a NAME="E9:19_6_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E10:19_6_4"/><b>then </b><i><font color="Green">E95</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#T26">SCMFSA_7:26</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E13:19"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmfsa7b.html#E9"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i>, , , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E96</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_6_5"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/><b>hence </b> <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T5" target="_self">Th5</a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E34:19_6"/><i><font color="Green">E97</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">c</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">c</font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_6"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:19_6_6"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E8:19"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmfsa7b.html#E9:19"><i><font color="Green">E39</font></i></a>, <a class="ref" href="scmfsa7b.html#T5" target="_self">Th5</a>, </i>;<br/>

<b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E2:19_6_6"/>
<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span>
 ;<br/>

<a NAME="E3:19_6_6"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#T28">SCMFSA_7:28</a></i>;<br/>
<a NAME="E4:19_6_6"/><b>then </b><i><font color="Green">E98</font></i>: 
<font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E5:19_6_6"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/>
<a NAME="E6:19_6_6"/>
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T2" target="_self">Th2</a>, , <a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/>
<a NAME="E7:19_6_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E8:19_6_6"/><b>then </b><i><font color="Green">E100</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E9:19_6_6"/><b>then </b>
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E10:19_6_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E11:19_6_6"/><b>then </b><i><font color="Green">E101</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#T26">SCMFSA_7:26</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="txt" href="scmfsa7b.html#E9"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i>, , , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E102</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_6_7"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span>
 ;<br/><b>hence </b> <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E13:19"><i><font color="Green">E45</font></i></a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green">E103</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_8"><b>now </b></a><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmfsa7b.html#E6:19"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/></div><b>end;</b></div>
<a NAME="E37:19_6"/><i><font color="Green">E104</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_9"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:19_6_9"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span>
 ;<br/>

<div><i><font color="Green">E106</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_9_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_6_9_1"/><i><font color="Green">E107</font></i>: 
not <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span>
 ;<br/><b>assume </b><a NAME="E2:19_6_9_1"/><i><font color="Green">E108</font></i>: 
(  not <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> or  not <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> )
 ;<br/><a NAME="E3:19_6_9_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><b>hence </b><a NAME="E4:19_6_9_1"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> )
 <b>by </b><i>, , , <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_9_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_6_9_2"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> or ( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> ) )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_9_2_1"><b>suppose </b></a><a NAME="E1:19_6_9_2_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_6_9_2_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_9_2_2"><b>suppose </b></a><a NAME="E1:19_6_9_2_2"/><i><font color="Green">E109</font></i>: 
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:19_6_9_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E3:19_6_9_2_2"/><b>then </b><i><font color="Green">E110</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E4:19_6_9_2_2"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>reconsider </b><font color="Maroon">ii</font> = <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E6:19_6_9_2_2"/>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">ii</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E8:19"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmfsa7b.html#E12:19"><i><font color="Green">E44</font></i></a>, </i>;<br/><b>hence </b><a NAME="E7:19_6_9_2_2"/>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_9_2_3"><b>suppose </b></a><a NAME="E1:19_6_9_2_3"/><i><font color="Green">E112</font></i>: 
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:19_6_9_2_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E3:19_6_9_2_3"/><b>then </b><i><font color="Green">E113</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E4:19_6_9_2_3"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>reconsider </b><font color="Maroon">ii</font> = <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><b>thus </b> <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">ii</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6" target="_self">Th6</a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span>

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

</div><b>end;</b></div>
<a NAME="E38:19_6"/><i><font color="Green">E115</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E39:19_6"/><b>then </b><i><font color="Green">E116</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E40:19_6"/><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E7:19"><i><font color="Green">E37</font></i></a>, <a class="ref" href="scmfsa7b.html#T4" target="_self">Th4</a></i>;<br/>
<div><i><font color="Green">E147</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_10"><b>now </b></a><div class="add"><a NAME="E1:19_6_10"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T84">FINSEQ_1:84</a></i>;<br/><b>hence </b><a NAME="E2:19_6_10"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div>
<a NAME="E42:19_6"/><i><font color="Green">E148</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<div><i><font color="Green">E149</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_11"><b>now </b></a><div class="add"><a NAME="E1:19_6_11"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E2:19_6_11"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><b>hence </b><a NAME="E3:19_6_11"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T2" target="_self">Th2</a>, , <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E150</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_12"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmfsa7b.html#E9"><i><font color="Green">Lemma48</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E7:19"><i><font color="Green">E37</font></i></a>, , , , <a class="ref" href="scmfsa_7.html#T18">SCMFSA_7:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T2" target="_self">Th2</a>, , </i>
<br/>.= 
<font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:19"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_1.html#T86">FINSEQ_1:86</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E151</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_13"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa7b.html#T2" target="_self">Th2</a>, , , <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T86">FINSEQ_1:86</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
<font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E152</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_14"><b>now </b></a><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E153</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_15"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</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="txt" href="scmfsa7b.html#E15:19"><i><font color="Green">E57</font></i></a>, <a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 2</span>)</span>,<font color="Maroon">pr1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scmfsa7b.html#E9"><i><font color="Green">Lemma48</font></i></a>, </i>
;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E48:19_6"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">i</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_6_16"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:19_6_16"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_16_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_6_16_1"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> or <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span> )
 </span><b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_16_1_1"><b>suppose </b></a><a NAME="E1:19_6_16_1_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_6_16_1_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E9"><i><font color="Green">Lemma48</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_6_16_1_2"><b>suppose </b></a><a NAME="E1:19_6_16_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp1</font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_6_16_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font>
 <b>by </b><i>, , , <a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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


</div><b>end;</b></div>
<a NAME="E17:19"/>
for <font color="Olive">r</font> being  <a href="finseq_1.html#NM1">FinSequence</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">r</font>]
 
<b>from </b><i><a class="ref" href="finseq_1.html#S3">FINSEQ_1:sch 3</a>(<a class="ref" href="scmfsa7b.html#T1" target="_self">Th1</a>, );<br/></i>
<b>then consider </b><font color="Maroon">pp0</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E19:19"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">pp0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">pp</font>
 <b>and </b><br/><a NAME="E20:19"/><i><font color="Green">E156</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp0</font></span>)</span></span>)</span> holds <br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">i</font>
 ;<br/>
<a NAME="E21:19"/><i><font color="Green">E158</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:19"><i><font color="Green">E26</font></i></a>, </i>;<br/>
<a NAME="E22:19"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E23:19"/><b>then </b><i><font color="Green">E159</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:19"><i><font color="Green">E28</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">f</font>,<font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">pp</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
;<br/>
<b>hence </b><a NAME="E25:19"/>
<font color="Maroon">s</font> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>


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