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

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="scmfsa_2.html#K4">intloc</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green">E10</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>



<a NAME="E3:16"/>
(  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmfsa_2.html#K4">intloc</a> 1 &amp;  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmfsa_2.html#K4">intloc</a> 2 )
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T16">SCMFSA_2:16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="scmfsa_2.html#K4">intloc</a> 1, <font color="Maroon">c<sub>8</sub></font> =  <a href="scmfsa_2.html#K4">intloc</a> 2 as  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a>  <b>by </b><i><a class="ref" href="sf_mastr.html#D5">SF_MASTR:def 5</a></i>;<br/>
<a NAME="E5:16"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T16">SCMFSA_2:16</a></i>;<br/>
<b>assume </b><a NAME="E6:16"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_7.html#K5">:=</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>9</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>;<br/>
<a NAME="E7:16"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_7.html#K5">:=</a> <font color="Maroon">c<sub>6</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#D5">SCMFSA_7:def 5</a></i>;<br/>
<a NAME="E8:16"/><i><font color="Green">E15</font></i>: 
 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="scmfsa_7.html#D1">SCMFSA_7:def 1</a></i>;<br/>
<div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E17</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:16_1"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&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">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_1"><i><font color="Green">E17</font></i></a>, <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_1"><i><font color="Green">E18</font></i></a>, <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">c<sub>11</sub></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="E11:16"/><i><font color="Green">E17</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E12:16"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span> )
 <b>and </b><br/><a NAME="E13:16"/><i><font color="Green">E19</font></i>: 
 <a href="scmfsa_7.html#K4">aSeq</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>11</sub></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">c<sub>12</sub></font> =  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E14:16"/><i><font color="Green">E20</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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="E15:16"/><i><font color="Green">E21</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><a NAME="E1:16_2"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E15:16"><i><font color="Green">E21</font></i></a>, <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E2:16_2"/><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_7.html#K5">:=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E7:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="scmfsa_7.html#T31">SCMFSA_7:31</a></i>;<br/><b>hence </b><a NAME="E3:16_2"/>
 <a href="scmfsa_7.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_3"/><i><font color="Green">E24</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:16_3"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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="E3:16_3"/>
<font color="Maroon">c<sub>4</sub></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">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&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">c<sub>13</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="scmfsa7b.html#E7:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><a NAME="E4:16_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></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">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scmfsa_7.html#D1">SCMFSA_7:def 1</a></i>;<br/><b>hence </b><a NAME="E5:16_3"/>
<font color="Maroon">c<sub>4</sub></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">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_3"><i><font color="Green">E25</font></i></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">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_4"/>
<font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:16_4"/><b>then </b><i><font color="Green">E25</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>14</sub></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">c<sub>13</sub></font></span>)</span> = 
<font color="Maroon">c<sub>4</sub></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">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E17:16"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16_4"><i><font color="Green">E25</font></i></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>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font> implies ex <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>2</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">b<sub>1</sub></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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>2</sub></font> ) &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> &amp;  <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>2</sub></font> ) ) );<br/>
<a NAME="E19:16"/><i><font color="Green">E25</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="16_5"><b>proof </b></a><div class="add">

<i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="E2:16_5"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<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="E3:16_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><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_5_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:16_5_2"/>
( <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> implies <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E3:16_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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scmfsa7b.html#E16:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_5_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmfsa_7.html#T37">SCMFSA_7:37</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:16_5"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E6:16_5"/><b>then </b><i><font color="Green">E28</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E4:16_5"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E7:16_5"/>
 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E15:16"><i><font color="Green">E21</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E8:16_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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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="E9:16_5"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E10:16_5"/><i><font color="Green">E30</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<i><font color="Green">E31</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16_5"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmfsa7b.html#E9:16_5"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E15:16"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmfsa7b.html#E10:16_5"><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">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
;<br/>
<i><font color="Green">E32</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <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">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16_5"><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">E33</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E12:16_5"><i><font color="Green">E32</font></i></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E14:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scmfsa7b.html#E6:16_5"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_5_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_5_6"/>
<font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:16_5_6"/><b>then </b>
( <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> or <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="E3:16_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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E4:16_5"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmfsa7b.html#E13:16_5"><i><font color="Green">E33</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E15:16_5"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_5"><i><font color="Green">E26</font></i></a></i>;<br/>

<a NAME="E16:16_5"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p2">(<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> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T32">FINSEQ_1:32</a></i>;<br/>
<b>hence </b><a NAME="E17:16_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <span class="p0">(<span class="default"><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></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</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>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T21">SCMFSA_7:21</a></i>;<br/>

<b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E19:16_5"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="finsop_1.html#K1">|-&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>;<br/>
<font color="Maroon">c<sub>13</sub></font> = 
 <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scmfsa7b.html#E16:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmfsa7b.html#E19:16_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmfsa_7.html#T37">SCMFSA_7:37</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="scmfsa_7.html#T1">SCMFSA_7:1</a></i>
;<br/>
<b>hence </b><a NAME="E21:16_5"/>
 <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <span class="p0">(<span class="default"><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></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_5"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmfsa7b.html#E12:16_5"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa7b.html#E19:16_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_5_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:16_5_8"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E12:16_5"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scmfsa7b.html#E16:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_5_8"><i><font color="Green">E35</font></i></a>, <a class="ref" href="scmfsa_7.html#T37">SCMFSA_7:37</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E23:16_5"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <span class="p5">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p0">(<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_5"><i><font color="Green">E26</font></i></a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_5_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>assume </b><a NAME="E1:16_5_9"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E12:16_5"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_5_9"><i><font color="Green">E35</font></i></a>, <a class="ref" href="scmfsa_2.html#T101">SCMFSA_2:101</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scmfsa7b.html#E16:16"><i><font color="Green">E22</font></i></a>, <a class="ref" href="scmfsa_7.html#T37">SCMFSA_7:37</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E25:16_5"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <span class="p5">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <span class="p0">(<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></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_5"><i><font color="Green">E26</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:16"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></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">b<sub>2</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:16_6"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>13</sub></font>]
 ;<br/>

<b>assume </b><a NAME="E2:16_6"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>13</sub></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">c<sub>14</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_1"><b>now </b></a><div class="add"><a NAME="E1:16_6_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>13</sub></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">c<sub>14</sub></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>hence </b><a NAME="E2:16_6_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon">c<sub>15</sub></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="E5:16_6"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>and </b><br/><a NAME="E6:16_6"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E7:16_6"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E8:16_6"/><i><font color="Green">E32</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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E9:16_6"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E10:16_6"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6"><i><font color="Green">E27</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/>
<div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_2"><b>now </b></a><div class="add"><a NAME="E1:16_6_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></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">c<sub>14</sub></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">c<sub>13</sub></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="E2:16_6_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>13</sub></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">c<sub>14</sub></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/><b>hence </b><a NAME="E3:16_6_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>13</sub></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">c<sub>14</sub></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/></div><b>end;</b></div>
<div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_3"><b>now </b></a><div class="add"><a NAME="E1:16_6_3"/>
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></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">c<sub>14</sub></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">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6"><i><font color="Green">E28</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E2:16_6_3"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16_6"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E13:16_6"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E14:16_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">c<sub>13</sub></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">c<sub>13</sub></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">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E16:16_6"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></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">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E17:16_6"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>11</sub></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">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E12:16"><i><font color="Green">E18</font></i></a></i>;<br/>
<div><i><font color="Green">E40</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_4"><b>now </b></a><div class="add"><b>thus </b><font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></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">c<sub>14</sub></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">c<sub>13</sub></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">c<sub>11</sub></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">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmfsa7b.html#E11:16_6"><i><font color="Green">E35</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E19:16_6"/><b>then </b>
( <font color="Maroon">c<sub>14</sub></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>  &amp; <font color="Maroon">c<sub>14</sub></font> is    <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#E12:16_6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E20:16_6"/><b>then </b>
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></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">c<sub>18</sub></font> = <font color="Maroon">c<sub>15</sub></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">c<sub>14</sub></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">c<sub>18</sub></font>
;<br/>

<b>thus </b><a NAME="E22:16_6"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></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">c<sub>14</sub></font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E5:16_6"><i><font color="Green">E29</font></i></a></i>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>14</sub></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#E12:16_6"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16_6"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E24:16_6"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E17:16_6"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16_6"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E25:16_6"/><i><font color="Green">E42</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>18</sub></font> <a href="tarski.html#R1">c=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:16_6"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmfsa_7.html#T19">SCMFSA_7:19</a></i>;<br/>
<div><i><font color="Green">E43</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_5"><b>now </b></a><div class="add"><b>thus </b> <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>18</sub></font> = 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>15</sub></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#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>19</sub></font></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="ref" href="dtconstr.html#T13">DTCONSTR:13</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E27:16_6"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>19</sub></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">c<sub>20</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>24</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E28:16_6"/><i><font color="Green">E45</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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="E29:16_6"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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="E30:16_6"/><i><font color="Green">E47</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E28:16_6"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E31:16_6"/><i><font color="Green">E48</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>assume </b><a NAME="E1:16_6_6"/>
<font color="Maroon">c<sub>25</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>19</sub></font>
 ;<br/><a NAME="E2:16_6_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>25</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="finseq_6.html#T15">FINSEQ_6:15</a></i>;<br/><a NAME="E3:16_6_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>25</sub></font> <a href="tarski.html#R1">c=</a>  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E25:16_6"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmfsa7b.html#E26:16_6"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E4:16_6_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_6.html#T15">FINSEQ_6:15</a></i>;<br/><a NAME="E5:16_6_6"/><b>then </b><i><font color="Green">E50</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/><a NAME="E6:16_6_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E13:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/><b>hence </b><a NAME="E7:16_6_6"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E5:16_6_6"><i><font color="Green">E50</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E33:16_6"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:16_6_7"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/>

<div><i><font color="Green">E52</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_7_1"><b>now </b></a><div class="add"><a NAME="E1:16_6_7_1"/>
 <a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E24:16_6"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/><b>hence </b><a NAME="E2:16_6_7_1"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E32:16_6"><i><font color="Green">E49</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:16_6_7"/><b>then </b><i><font color="Green">E53</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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="E4:16_6_7"/><i><font color="Green">E54</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font> <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_7"><i><font color="Green">E51</font></i></a>, <a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/>
<a NAME="E5:16_6_7"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E8:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="scmfsa7b.html#E3:16_6_7"><i><font color="Green">E53</font></i></a></i>;<br/>
<div><i><font color="Green">E56</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_7_2"><b>now </b></a><div class="add"><a NAME="E1:16_6_7_2"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E4:16_6_7"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E2:16_6_7_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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><b>hence </b><a NAME="E3:16_6_7_2"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font>
 ;<br/></div><b>end;</b></div>
<b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>25</sub></font> = 
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_7"><i><font color="Green">E51</font></i></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6_7"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:16_6_7"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa7b.html#E6:16_6_7"><i><font color="Green">E56</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E9:16"><i><font color="Green">E16</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:16_6_7"><i><font color="Green">E55</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="scmfsa7b.html#E7:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:16_6_7"><i><font color="Green">E55</font></i></a>, <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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</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>
<a NAME="E34:16_6"/><i><font color="Green">E51</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp;  <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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scmfsa7b.html#E6:16_6"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmfsa7b.html#E9:16_6"><i><font color="Green">E33</font></i></a></i>;<br/>
<div><i><font color="Green">E52</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_6_8"/>
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E33:16_6"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16_6"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>25</sub></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">E53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_6_9"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span>
 ;<br/><a NAME="E2:16_6_9"/><b>then </b><i><font color="Green">E55</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font> <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/><div><i><font color="Green">E56</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_9_1"><b>now </b></a><div class="add"><a NAME="E1:16_6_9_1"/>
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E17:16_6"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16_6"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_6.html#T12">FINSEQ_6:12</a></i>;<br/><a NAME="E2:16_6_9_1"/><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E32:16_6"><i><font color="Green">E49</font></i></a></i>;<br/><b>hence </b><a NAME="E3:16_6_9_1"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_9_2"><b>now </b></a><div class="add"><a NAME="E1:16_6_9_2"/>
 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E3:16_6_9"><i><font color="Green">E56</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><b>hence </b><a NAME="E2:16_6_9_2"/>
 <a href="scmfsa_2.html#K5">insloc</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E8:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16_6_9"><i><font color="Green">E55</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_9_3"><b>now </b></a><div class="add"><a NAME="E1:16_6_9_3"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6_9"><i><font color="Green">E55</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font>

;<br/><br/></div><b>end;</b></div><b>thus </b><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>25</sub></font> = 
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_9"><i><font color="Green">E54</font></i></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6_9"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmfsa7b.html#E3:16_6_9"><i><font color="Green">E56</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&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#K13">*&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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E9:16"><i><font color="Green">E16</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:16_6_9"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:16_6_9"><i><font color="Green">E58</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="scmfsa7b.html#E7:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:16_6_9"><i><font color="Green">E57</font></i></a>, <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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</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>
<a NAME="E37:16_6"/><i><font color="Green">E54</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp;  <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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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#E28:16_6"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmfsa7b.html#E29:16_6"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmfsa7b.html#E33:16_6"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16_6"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>;<br/>
<div><i><font color="Green">E55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_6_10"/>
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>25</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E36:16_6"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa7b.html#E37:16_6"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>25</sub></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">E56</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_11"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E24:16_6"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmfsa7b.html#E26:16_6"><i><font color="Green">E43</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11"><i><font color="Green">Lemma7</font></i></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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/></div><b>end;</b></div>
<div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_12"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E39:16_6"><i><font color="Green">E56</font></i></a>, <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/></div><b>end;</b></div>
<a NAME="E41:16_6"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_13"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:16_6_13"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span>
 ;<br/>

<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_6_13_1"/><i><font color="Green">E61</font></i>: 
not <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span>
 ;<br/><b>assume </b><a NAME="E2:16_6_13_1"/><i><font color="Green">E62</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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">c<sub>25</sub></font> or  not <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> )
 ;<br/><a NAME="E3:16_6_13_1"/>
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_13"><i><font color="Green">E59</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><b>hence </b><a NAME="E4:16_6_13_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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E40:16_6"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_13_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16_6_13_1"><i><font color="Green">E62</font></i></a>, <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="16_6_13_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_6_13_2"/>
( <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> ) )
 </span><b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6_13"><i><font color="Green">E60</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_13_2_1"><b>suppose </b></a><a NAME="E1:16_6_13_2_1"/>
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_6_13_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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16_6"><i><font color="Green">E30</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_13_2_2"><b>suppose </b></a><a NAME="E1:16_6_13_2_2"/><i><font color="Green">E61</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:16_6_13_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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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="E3:16_6_13_2_2"/><b>then </b><i><font color="Green">E62</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E4:16_6_13_2_2"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_13_2_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="scmfsa7b.html#E3:16_6_13_2_2"><i><font color="Green">E62</font></i></a>, <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">c<sub>25</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E28:16_6"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmfsa7b.html#E35:16_6"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:16_6_13_2_2"><i><font color="Green">E63</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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span>

;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_13_2_3"><b>suppose </b></a><a NAME="E1:16_6_13_2_3"/><i><font color="Green">E61</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:16_6_13_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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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="E3:16_6_13_2_3"/><b>then </b><i><font color="Green">E62</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E4:16_6_13_2_3"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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#E1:16_6_13_2_3"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="scmfsa7b.html#E3:16_6_13_2_3"><i><font color="Green">E62</font></i></a>, <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">c<sub>25</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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<sub>26</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E38:16_6"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmfsa7b.html#E4:16_6_13_2_3"><i><font color="Green">E63</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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span>

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

</div><b>end;</b></div>
<a NAME="E42:16_6"/><i><font color="Green">E59</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E40:16_6"><i><font color="Green">E57</font></i></a>, <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="E43:16_6"/><b>then </b><i><font color="Green">E60</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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="E44:16_6"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&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#K13">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E27:16_6"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmfsa7b.html#E32:16_6"><i><font color="Green">E49</font></i></a></i>;<br/>
<div><i><font color="Green">E62</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_14"><b>now </b></a><div class="add"><a NAME="E1:16_6_14"/>
 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E44:16_6"><i><font color="Green">E61</font></i></a>, <a class="ref" href="finseq_1.html#T84">FINSEQ_1:84</a></i>;<br/><b>hence </b><a NAME="E2:16_6_14"/>
<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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div>
<a NAME="E46:16_6"/><i><font color="Green">E63</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#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">E64</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_15"><b>now </b></a><div class="add"><a NAME="E1:16_6_15"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="E2:16_6_15"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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="E3:16_6_15"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E17:16_6"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16_6"><i><font color="Green">E40</font></i></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">E65</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_16"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E41:16_6"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmfsa7b.html#E43:16_6"><i><font color="Green">E60</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#E18:16"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E45:16_6"><i><font color="Green">E62</font></i></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa7b.html#E44:16_6"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmfsa_7.html#T18">SCMFSA_7:18</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E66</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_17"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>19</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E27:16_6"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmfsa7b.html#E48:16_6"><i><font color="Green">E65</font></i></a>, <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>19</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E30:16_6"><i><font color="Green">E47</font></i></a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E67</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_18"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>19</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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">c<sub>19</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E17:16_6"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16_6"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa7b.html#E49:16_6"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmfsa7b.html#E12"><i><font color="Green">Lemma8</font></i></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E17:16_6"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmfsa7b.html#E18:16_6"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmfsa7b.html#E47:16_6"><i><font color="Green">E64</font></i></a>, <a class="ref" href="finseq_1.html#T86">FINSEQ_1:86</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E46:16_6"><i><font color="Green">E63</font></i></a>, <a class="ref" href="finseq_1.html#T86">FINSEQ_1:86</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font>
<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">E68</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_19"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E50:16_6"><i><font color="Green">E67</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E52:16_6"/><b>then </b><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<div><i><font color="Green">E70</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_20"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa7b.html#E51:16_6"><i><font color="Green">E68</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E41:16_6"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmfsa7b.html#E43:16_6"><i><font color="Green">E60</font></i></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"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>
;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E54:16_6"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_21"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:16_6_21"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_21_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_6_21_1"/>
( <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span> or <font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span> )
 </span><b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_21"><i><font color="Green">E71</font></i></a>, <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="16_6_21_1_1"><b>suppose </b></a><a NAME="E1:16_6_21_1_1"/>
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_6_21_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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E41:16_6"><i><font color="Green">E58</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_21_1_2"><b>suppose </b></a><a NAME="E1:16_6_21_1_2"/>
<font color="Maroon">c<sub>25</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_6_21_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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E53:16_6"><i><font color="Green">E70</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>consider </b><font color="Maroon">c<sub>25</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E56:16_6"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a>  <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="scmfsa_2.html#K17">:=</a> <font color="Maroon">c<sub>8</sub></font></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font> <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <font color="Maroon">c<sub>25</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>;<br/>
<div><i><font color="Green">E72</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_22"><b>now </b></a><div class="add"><b>thus </b><font color="Maroon">c<sub>25</sub></font> = 
 <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</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"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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="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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E56:16_6"><i><font color="Green">E71</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
 <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
 <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E5:16"><i><font color="Green">E12</font></i></a>, <a class="txt" href="scmfsa7b.html#E36:16_6"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa7b.html#E37:16_6"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>
<br/>.= 
 <a href="int_2.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E29:16_6"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmfsa7b.html#E33:16_6"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16_6"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmfsa_7.html#T1">SCMFSA_7:1</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E73</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_23"><b>now </b></a><div class="add"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></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">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E16:16_6"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmfsa7b.html#E36:16_6"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa7b.html#E37:16_6"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E74</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_24"><b>now </b></a><div class="add"><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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E36:16_6"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa7b.html#E37:16_6"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E29:16_6"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmfsa7b.html#E33:16_6"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16_6"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E60:16_6"/><i><font color="Green">E75</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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</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"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/>
<a NAME="E61:16_6"/><b>then </b><i><font color="Green">E76</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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E62:16_6"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:16_6"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_1.html#T84">FINSEQ_1:84</a></i>;<br/>
<a NAME="E63:16_6"/><b>then </b><i><font color="Green">E77</font></i>: 
 <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">c<sub>18</sub></font></span>)</span> <a href="tarski.html#R1">c=</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">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#T7">FINSEQ_1:7</a></i>;<br/>
<div><i><font color="Green">E78</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_25"><b>now </b></a><div class="add"><a NAME="E1:16_6_25"/>
 <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"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</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">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E8:16_6"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa7b.html#E51:16_6"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmfsa7b.html#E56:16_6"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmfsa7b.html#E57:16_6"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmfsa7b.html#E58:16_6"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scmfsa7b.html#E59:16_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmfsa7b.html#E60:16_6"><i><font color="Green">E75</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E2:16_6_25"/>
 <a href="relat_1.html#K1">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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</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">c<sub>18</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E63:16_6"><i><font color="Green">E77</font></i></a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E79</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_26"><b>now </b></a><div class="add"><a NAME="E1:16_6_26"/>
 <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">c<sub>18</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E63:16_6"><i><font color="Green">E77</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E2:16_6_26"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</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">c<sub>18</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/></div><b>end;</b></div>
<a NAME="E66:16_6"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <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">c<sub>18</sub></font></span>)</span> holds <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_27"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>26</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:16_6_27"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <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">c<sub>18</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:16_6_27"/><b>then </b><i><font color="Green">E81</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:16_6_27"/><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmfsa7b.html#E8:16_6"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa7b.html#E13:16_6"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_27_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_6_27_1"/>
( <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font> or <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_27_1_1"><b>suppose </b></a><a NAME="E1:16_6_27_1_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font>
 ;<br/><div class="add"><a NAME="E2:16_6_27_1_1"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></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="E3:16_6_27_1_1"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <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">c<sub>18</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_27_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="finseq_1.html#T6">FINSEQ_1:6</a></i>;<br/><b>hence </b><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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E52:16_6"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmfsa7b.html#E56:16_6"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmfsa7b.html#E57:16_6"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmfsa7b.html#E58:16_6"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scmfsa7b.html#E59:16_6"><i><font color="Green">E74</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></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">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E5:16_6"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmfsa7b.html#E3:16_6_27"><i><font color="Green">E82</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16_6_27_1_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E5:16_6"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:16_6_27_1_1"><i><font color="Green">E84</font></i></a>, <a class="txt" href="scmfsa7b.html#E3:16_6_27_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_6_27_1_2"><b>suppose </b></a><a NAME="E1:16_6_27_1_2"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font>
 ;<br/><div class="add"><a NAME="E2:16_6_27_1_2"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E5:16_6"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/><a NAME="E3:16_6_27_1_2"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6_27"><i><font color="Green">E81</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_27_1_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E4:16_6_27_1_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>26</sub></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> <font color="Maroon">c<sub>15</sub></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="E5:16_6_27_1_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:16_6_27_1_2"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <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">c<sub>15</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_6_27_1_2_1"><b>now </b></a><div class="add"><b>thus </b><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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_7.html#K2">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E52:16_6"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmfsa7b.html#E56:16_6"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmfsa7b.html#E57:16_6"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmfsa7b.html#E58:16_6"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scmfsa7b.html#E59:16_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_27"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:16_6_27_1_2"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
;<br/></div><b>end;</b></div><b>hence </b><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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E7:16_6"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa7b.html#E6:16_6_27_1_2"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E6:16_6_27_1_2"><i><font color="Green">E85</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E1:16_6_27"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E67:16_6"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <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">c<sub>18</sub></font></span>)</span> holds <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E68:16_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E64:16_6"><i><font color="Green">E78</font></i></a>, <a class="txt" href="scmfsa7b.html#E65:16_6"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>

<b>thus </b><a NAME="E69:16_6"/>
 <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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E8:16_6"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa7b.html#E51:16_6"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmfsa7b.html#E56:16_6"><i><font color="Green">E71</font></i></a>, <a class="txt" href="scmfsa7b.html#E57:16_6"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmfsa7b.html#E58:16_6"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scmfsa7b.html#E59:16_6"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmfsa7b.html#E61:16_6"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>26</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:16_6_28"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa7b.html#E51:16_6"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E36:16_6"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa7b.html#E37:16_6"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_28"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E29:16_6"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmfsa7b.html#E33:16_6"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16_6"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_28"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E9:16_6"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_28"><i><font color="Green">E80</font></i></a></i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>26</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>assume </b><a NAME="E1:16_6_29"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E31:16_6"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmfsa7b.html#E42:16_6"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmfsa7b.html#E51:16_6"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmfsa_2.html#T99">SCMFSA_2:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></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> <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> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E36:16_6"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmfsa7b.html#E37:16_6"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E29:16_6"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmfsa7b.html#E33:16_6"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16_6"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmfsa_7.html#T36">SCMFSA_7:36</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E10:16_6"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:16_6_29"><i><font color="Green">E80</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E21:16"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="finseq_1.html#S3">FINSEQ_1:sch 3</a>(<a class="txt" href="scmfsa7b.html#E19:16"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmfsa7b.html#E20:16"><i><font color="Green">E26</font></i></a>);<br/></i>
<b>then consider </b><font color="Maroon">c<sub>13</sub></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="E23:16"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E24:16"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>13</sub></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">c<sub>4</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E25:16"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>13</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E26:16"/><i><font color="Green">E30</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="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>13</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E27:16"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>13</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E28:16"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>13</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>
<a NAME="E29:16"/><i><font color="Green">E33</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E23:16"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmfsa7b.html#E24:16"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E30:16"/>
 <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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E13:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E31:16"/><b>then </b><i><font color="Green">E34</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<i><font color="Green">E35</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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></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">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E29:16"><i><font color="Green">E33</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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&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#K13">*&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> <font color="Maroon">c<sub>7</sub></font>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></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#E18:16"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmfsa7b.html#E31:16"><i><font color="Green">E34</font></i></a></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="txt" href="scmfsa7b.html#E13:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
;<br/>
<b>hence </b><a NAME="E33:16"/>
<font color="Maroon">c<sub>4</sub></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/>

<a NAME="E34:16"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E32:16"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_1.html#D22">AMI_1:def 22</a></i>;<br/>
<a NAME="E35:16"/>
 <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"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa_2.html#K19">:=&lt;0,...,0&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="binarith.html#K13">*&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">c<sub>13</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</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">c<sub>13</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmfsa7b.html#E23:16"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmfsa7b.html#E26:16"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E36:16"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E23:16"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmfsa7b.html#E25:16"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16"><i><font color="Green">E36</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>
<a NAME="E37:16"/>
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</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">c<sub>13</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E11:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmfsa7b.html#E23:16"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E38:16"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E36:16"><i><font color="Green">E37</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>

<b>thus </b><a NAME="E39:16"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M1">Int-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmfsa_2.html#K4">intloc</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmfsa_2.html#K4">intloc</a> 2 holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="scmfsa_2.html#M2">FinSeq-Location</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E23:16"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmfsa7b.html#E27:16"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmfsa7b.html#E28:16"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmfsa7b.html#E34:16"><i><font color="Green">E36</font></i></a></i>;<br/>


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