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

<a NAME="E1:36"/><i><font color="Green">E29</font></i>: 
 <a href="finseq_2.html#K1">idseq</a> 3 <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">1,2,3</span><a href="finseq_4.html#K3">*&gt;</a></span> as  <a href="funct_1.html#V2">one-to-one</a> <a href="finseq_1.html#V1">FinSequence-like</a> <a href="funct_2.html#NM1">Function</a> of  <a href="setwop_2.html#K2">Seg</a> 3, <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="ref" href="finseq_2.html#T62">FINSEQ_2:62</a></i>;<br/>
<a NAME="E3:36"/><i><font color="Green">E30</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">1,3,2</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>2</sub></font> = <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">2,3</span><a href="finseq_4.html#K2">*&gt;</a></span>;<br/>
<a NAME="E1:36_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default">1</span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">2,3</span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>;<br/>
<a NAME="E2:36_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E1"><i><font color="Green">Lemma1</font></i></a>, <a class="ref" href="finseq_2.html#T62">FINSEQ_2:62</a></i>;<br/>
<a NAME="E3:36_1"/>
 <a href="finseq_5.html#K4">Rev</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">2,3</span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">3,2</span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T64">FINSEQ_5:64</a></i>;<br/>
<a NAME="E4:36_1"/><b>then </b>
<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default">1</span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default">2,3</span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">1,3,2</span><a href="finseq_4.html#K3">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>;<br/>
<b>hence </b><a NAME="E5:36_1"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">1,3,2</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 <b>by </b><i><a class="txt" href="matrix_9.html#E1:36_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="matrix_9.html#E2:36_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="matrix_9.html#T17" target="_self">Th17</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:36"/><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">2,3,1</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>proof </b></a><div class="add">

<a NAME="E1:36_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default">1</span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">2,3</span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>;<br/>
<b>hence </b><a NAME="E2:36_2"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">2,3,1</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 <b>by </b><i><a class="ref" href="matrix_9.html#T18" target="_self">Th18</a>, <a class="txt" href="matrix_9.html#E1:36"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_2.html#T62">FINSEQ_2:62</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">1,2</span><a href="finseq_4.html#K2">*&gt;</a></span>;<br/>
<a NAME="E5:36"/><i><font color="Green">E32</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">2,1,3</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_3"><b>proof </b></a><div class="add">

<a NAME="E1:36_3"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default">3</span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">1,2</span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E1:36"><i><font color="Green">E29</font></i></a>, <a class="ref" href="matrix_9.html#T18" target="_self">Th18</a>, <a class="ref" href="finseq_2.html#T62">FINSEQ_2:62</a></i>;<br/>
<a NAME="E2:36_3"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">1,2</span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">2,1</span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T64">FINSEQ_5:64</a></i>;<br/>
<a NAME="E3:36_3"/>
<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default">3</span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default">1,2</span><a href="finseq_4.html#K2">*&gt;</a></span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<b>by </b><i><a class="ref" href="matrix_9.html#T17" target="_self">Th17</a>, <a class="txt" href="matrix_9.html#E1:36_3"><i><font color="Green">E33</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:36_3"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">2,1,3</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 <b>by </b><i><a class="ref" href="matrix_9.html#T18" target="_self">Th18</a>, <a class="txt" href="matrix_9.html#E2:36_3"><i><font color="Green">E34</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:36"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">3,1,2</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_4"><b>proof </b></a><div class="add">

<a NAME="E1:36_4"/>
<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default">3</span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default">1,2</span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">3,1,2</span><a href="finseq_4.html#K3">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>;<br/>
<b>hence </b><a NAME="E2:36_4"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">3,1,2</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 <b>by </b><i><a class="ref" href="matrix_9.html#T18" target="_self">Th18</a>, <a class="txt" href="matrix_9.html#E1:36"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_2.html#T62">FINSEQ_2:62</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:36"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">3,2,1</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3
 
<b>by </b><i><a class="ref" href="matrix_9.html#T15" target="_self">Th15</a>, <a class="ref" href="matrix_9.html#T5" target="_self">Th5</a>, <a class="txt" href="matrix_9.html#E1:36"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:36"/>
( <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">1,3,2</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3 &amp; <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">2,3,1</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3 &amp; <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">2,1,3</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3 &amp; <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">3,1,2</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3 &amp; <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">1,2,3</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3 &amp; <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default">3,2,1</span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_2.html#K11">Permutations</a> 3 )
 <b>by </b><i><a class="txt" href="matrix_9.html#E3:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrix_9.html#E4:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="matrix_9.html#E5:36"><i><font color="Green">E32</font></i></a>, <a class="txt" href="matrix_9.html#E6:36"><i><font color="Green">E33</font></i></a>, <a class="ref" href="finseq_2.html#T62">FINSEQ_2:62</a>, <a class="txt" href="matrix_9.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>


</div>
