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

<b>set </b><font color="Maroon">f</font> = <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>;<br/>
<b>set </b><font color="Maroon">g</font> = <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>;<br/>
<b>set </b><font color="Maroon">h</font> = <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>;<br/>
<b>set </b><font color="Maroon">F</font> = <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>;<br/>
<b>set </b><font color="Maroon">G</font> = <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>;<br/>
<b>set </b><font color="Maroon">H</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>;<br/>
<a NAME="E1:46"/>
 <a href="setwop_2.html#K3">dom</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> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/>
<a NAME="E2:46"/><b>then </b><i><font color="Green">E31</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</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> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</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> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</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="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E3:46"/>
 <a href="setwop_2.html#K3">dom</a> <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#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/>
<a NAME="E4:46"/><b>then </b><i><font color="Green">E34</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E5:46"/>
 <a href="setwop_2.html#K3">dom</a> <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#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/>
<a NAME="E6:46"/><b>then </b><i><font color="Green">E37</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E7:46"/>
 <a href="setwop_2.html#K3">dom</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> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/>
<a NAME="E8:46"/><b>then </b><i><font color="Green">E38</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</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> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</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> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</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="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E9:46"/>
 <a href="setwop_2.html#K3">dom</a> <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#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T30">FINSEQ_3:30</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/>
<a NAME="E10:46"/><b>then </b><i><font color="Green">E39</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <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> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E11:46"/><i><font color="Green">E40</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#K12">Permutations</a> 3 &amp; <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#K12">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#K12">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#K12">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#K12">Permutations</a> 3 )
 
<b>by </b><i><a class="ref" href="matrix_9.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E12:46"/><i><font color="Green">E41</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> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</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> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</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> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</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> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 &amp; <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> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 )
 
<b>by </b><i><a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a>, <a class="ref" href="matrix_9.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E13:46"/><i><font color="Green">E42</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> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E15:46"><i><font color="Green">E43</font></i></a>, <a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <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>, <font color="Maroon">g</font> = <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>, <font color="Maroon">h</font> = <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>, <font color="Maroon">F</font> = <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>, <font color="Maroon">G</font> = <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> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, </i>;<br/>
<a NAME="E15:46"/><i><font color="Green">E43</font></i>: 
( 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> &amp; 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> &amp; 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> &amp; 3 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">gf</font> = <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E18:46"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E17:46"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">f</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 &amp; <font color="Maroon">g</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 &amp; <font color="Maroon">h</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 &amp; <font color="Maroon">G</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 &amp; <font color="Maroon">F</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> 3 )
 
<b>by </b><i><a class="txt" href="matrix_9.html#E15:46"><i><font color="Green">E43</font></i></a>, <a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/>
<a NAME="E18:46"/><i><font color="Green">E45</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gf</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fg</font> = <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E20:46"/><i><font color="Green">E72</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">fg</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fF</font> = <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">F</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E22:46"/><i><font color="Green">E73</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">fF</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">fh</font> = <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">h</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E24:46"/><i><font color="Green">E74</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">fh</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">hf</font> = <font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E26:46"/><i><font color="Green">E75</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">hf</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">FF</font> = <font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">F</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E28:46"/><i><font color="Green">E76</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">FF</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">FG</font> = <font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">G</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E30:46"/><i><font color="Green">E78</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">FG</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">GF</font> = <font color="Maroon">G</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">F</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E32:46"/><i><font color="Green">E79</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">GF</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">GG</font> = <font color="Maroon">G</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">G</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E17:46"><i><font color="Green">E44</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E34:46"/><i><font color="Green">E81</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">GG</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">gG</font> = <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">G</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<b>reconsider </b><font color="Maroon">gh</font> = <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">h</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E37:46"/><i><font color="Green">E82</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gh</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">hg</font> = <font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E39:46"/><i><font color="Green">E83</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">hg</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">hh</font> = <font color="Maroon">h</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">h</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E41:46"/><i><font color="Green">E84</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">hh</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">gg</font> = <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E43:46"/><i><font color="Green">E86</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gg</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">ff</font> = <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="setwop_2.html#K2">Seg</a> 3 <b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T50">FINSEQ_2:50</a></i>;<br/>
<a NAME="E45:46"/><i><font color="Green">E87</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">ff</font> <a href="hidden.html#R1">=</a> 3
 
<b>by </b><i><a class="txt" href="matrix_9.html#E4"><i><font color="Green">Lemma47</font></i></a>, <a class="txt" href="matrix_9.html#E3"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="finseq_2.html#T47">FINSEQ_2:47</a></i>;<br/>
<b>thus </b><a NAME="E46:46"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>proof </b></a><div class="add">

<i><font color="Green">E88</font></i>: <font color="Maroon">gf</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E141</font></i>: <font color="Maroon">gf</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">gf</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_1"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <b>by </b><i><a class="txt" href="matrix_9.html#E5"><i><font color="Green">Lemma48</font></i></a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E47:46"/>
<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="partfun1.html#K1">*</a> <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#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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>proof </b></a><div class="add">

<i><font color="Green">E142</font></i>: <font color="Maroon">fg</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E143</font></i>: <font color="Maroon">fg</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">fg</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_2"/>
<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="partfun1.html#K1">*</a> <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#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="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E48:46"/>
<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="partfun1.html#K1">*</a> <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#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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_3"><b>proof </b></a><div class="add">

<i><font color="Green">E144</font></i>: <font color="Maroon">gh</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E145</font></i>: <font color="Maroon">gh</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">gh</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_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="partfun1.html#K1">*</a> <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#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="matrix_9.html#T4" target="_self">Th4</a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E49:46"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4"><b>proof </b></a><div class="add">

<i><font color="Green">E146</font></i>: <font color="Maroon">hg</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E147</font></i>: <font color="Maroon">hg</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">hg</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_4"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <b>by </b><i><a class="ref" href="matrix_9.html#T5" target="_self">Th5</a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E50:46"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_5"><b>proof </b></a><div class="add">

<i><font color="Green">E148</font></i>: <font color="Maroon">hh</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E149</font></i>: <font color="Maroon">hh</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">hh</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_5"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <b>by </b><i><a class="ref" href="matrix_9.html#T6" target="_self">Th6</a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E51:46"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_6"><b>proof </b></a><div class="add">

<i><font color="Green">E150</font></i>: <font color="Maroon">gg</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E151</font></i>: <font color="Maroon">gg</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">gg</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E11:46"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_6"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <b>by </b><i>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E52:46"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7"><b>proof </b></a><div class="add">

<i><font color="Green">E152</font></i>: <font color="Maroon">ff</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E153</font></i>: <font color="Maroon">ff</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">ff</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_7"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <b>by </b><i>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E53:46"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_8"><b>proof </b></a><div class="add">

<i><font color="Green">E154</font></i>: <font color="Maroon">fF</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E155</font></i>: <font color="Maroon">fF</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">fF</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_8"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <b>by </b><i>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E54:46"/>
<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="partfun1.html#K1">*</a> <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#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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_9"><b>proof </b></a><div class="add">

<i><font color="Green">E156</font></i>: <font color="Maroon">FF</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E157</font></i>: <font color="Maroon">FF</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">FF</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_9"/>
<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="partfun1.html#K1">*</a> <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#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="txt" href="matrix_9.html#E6"><i><font color="Green">Lemma53</font></i></a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E55:46"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10"><b>proof </b></a><div class="add">

<i><font color="Green">E158</font></i>: <font color="Maroon">FG</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E12:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E159</font></i>: <font color="Maroon">FG</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E12:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">FG</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E12:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_10"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <b>by </b><i>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E56:46"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11"><b>proof </b></a><div class="add">

<i><font color="Green">E160</font></i>: <font color="Maroon">GF</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E161</font></i>: <font color="Maroon">GF</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">GF</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E10:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_11"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <b>by </b><i><a class="ref" href="matrix_9.html#T2" target="_self">Th2</a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E57:46"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12"><b>proof </b></a><div class="add">

<i><font color="Green">E162</font></i>: <font color="Maroon">GG</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E12:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E163</font></i>: <font color="Maroon">GG</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E12:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">GG</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E12:46"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_12"/>
<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="partfun1.html#K1">*</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> <a href="hidden.html#R1">=</a> <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>
 <b>by </b><i><a class="ref" href="matrix_9.html#T3" target="_self">Th3</a>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E58:46"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13"><b>proof </b></a><div class="add">

<i><font color="Green">E164</font></i>: <font color="Maroon">fh</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E165</font></i>: <font color="Maroon">fh</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">fh</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E13:46"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_13"/>
<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="partfun1.html#K1">*</a> <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#R1">=</a> <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>
 <b>by </b><i>, , <a class="ref" href="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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

<b>thus </b><a NAME="E59:46"/>
<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="partfun1.html#K1">*</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> <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_14"><b>proof </b></a><div class="add">

<i><font color="Green">E166</font></i>: <font color="Maroon">hf</font> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green">E167</font></i>: <font color="Maroon">hf</font> <a href="funct_1.html#K1">.</a> 2 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 3
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<font color="Maroon">hf</font> <a href="funct_1.html#K1">.</a> 3 = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="matrix_9.html#E8:46"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:46_14"/>
<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="partfun1.html#K1">*</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> <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="matrix_9.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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


</div>
