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

<b>let </b><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:14_1_2"/><i><font color="Green" title="E10">A7</font></i>: 
 ex <font color="Olive" title="b1">pp</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">pp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> &amp; ( for <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> holds <br/> ex <font color="Olive" title="b3">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b1">pp</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<font color="Olive" title="b2">k</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Olive" title="b3">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) ) &amp; <font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Olive" title="b1">pp</font> )
 <b>and </b><br/><a NAME="E2:14_1_2"/><i><font color="Green" title="E11">A8</font></i>: 
 ex <font color="Olive" title="b1">pp</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">pp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> &amp; ( for <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> holds <br/> ex <font color="Olive" title="b3">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b1">pp</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<font color="Olive" title="b2">k</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Olive" title="b3">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> ) ) &amp; <font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Olive" title="b1">pp</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">pp1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> <b> such that </b><br/><a NAME="E4:14_1_2"/><i><font color="Green" title="E12">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">pp1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E5:14_1_2"/><i><font color="Green" title="E13">A10</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> holds <br/> ex <font color="Olive" title="b2">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> &amp; <font color="Maroon" title="c5">pp1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<font color="Olive" title="b1">k</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 <b>and </b><br/><a NAME="E6:14_1_2"/><i><font color="Green" title="E14">A11</font></i>: 
<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Maroon" title="c5">pp1</font>
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E1:14_1_2"><i><font color="Green" title="E10">A7</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">pp2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> <b> such that </b><br/><a NAME="E8:14_1_2"/><i><font color="Green" title="E15">A12</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pp2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E9:14_1_2"/><i><font color="Green" title="E16">A13</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> holds <br/> ex <font color="Olive" title="b2">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> &amp; <font color="Maroon" title="c6">pp2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<font color="Olive" title="b1">k</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Olive" title="b2">i</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 <b>and </b><br/><a NAME="E10:14_1_2"/><i><font color="Green" title="E17">A14</font></i>: 
<font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dtconstr.html#K15" title="DTCONSTR:func.15">FlattenSeq</a> <font color="Maroon" title="c6">pp2</font>
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E2:14_1_2"><i><font color="Green" title="E11">A8</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">i</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E12:14_1_2"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">pp1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pp2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i</font> &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">pp1</font> holds <br/><font color="Maroon" title="c5">pp1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pp2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:14_1_2_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">pp1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pp2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i</font> )
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E4:14_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="scmfsa_7.html#E8:14_1_2"><i><font color="Green" title="E15">A12</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c8">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><a NAME="E1:14_1_2_1_1"/><i><font color="Green" title="E18">A15</font></i>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><b>assume </b><a NAME="E2:14_1_2_1_1"/>
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">pp1</font>
 ;<br/><a NAME="E3:14_1_2_1_1"/><b>then </b><i><font color="Green" title="E19">A16</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p</font> )
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E4:14_1_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">i1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E5:14_1_2_1_1"/><i><font color="Green" title="E20">A17</font></i>: 
( <font color="Maroon" title="c9">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c5">pp1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<font color="Maroon" title="c8">k</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c9">i1</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E5:14_1_2"><i><font color="Green" title="E13">A10</font></i></a>, <a class="txt" href="scmfsa_7.html#E1:14_1_2_1_1"><i><font color="Green" title="E18">A15</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c10">i2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E7:14_1_2_1_1"/><i><font color="Green" title="E21">A18</font></i>: 
( <font color="Maroon" title="c10">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c6">pp2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<font color="Maroon" title="c8">k</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c10">i2</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E9:14_1_2"><i><font color="Green" title="E16">A13</font></i></a>, <a class="txt" href="scmfsa_7.html#E1:14_1_2_1_1"><i><font color="Green" title="E18">A15</font></i></a>, <a class="txt" href="scmfsa_7.html#E3:14_1_2_1_1"><i><font color="Green" title="E19">A16</font></i></a></i>;<br/><b>thus </b><a NAME="E8:14_1_2_1_1"/>
<font color="Maroon" title="c5">pp1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pp2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E5:14_1_2_1_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="txt" href="scmfsa_7.html#E7:14_1_2_1_1"><i><font color="Green" title="E21">A18</font></i></a></i>;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<b>hence </b><a NAME="E13:14_1_2"/>
<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font>
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E6:14_1_2"><i><font color="Green" title="E14">A11</font></i></a>, <a class="txt" href="scmfsa_7.html#E10:14_1_2"><i><font color="Green" title="E17">A14</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


</div>
