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<b>let </b><font color="Maroon">l</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> 3</span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">l</font></span>)</span> <a href="nat_1.html#K6">mod</a> 2 <a href="hidden.html#R1">=</a> 0
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">i</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <font color="Maroon">l</font> holds <br/> ex <font color="Olive">q</font> being   <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K12">Permutations</a> 3 st <br/>( <font color="Maroon">l</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">q</font> &amp; <font color="Olive">q</font> <a href="matrix_2.html#NR1" target="_self">is_transposition</a>  )
 ;<br/>

<a NAME="E3:55"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <font color="Maroon">l</font> holds <br/> ex <font color="Olive">q</font> being   <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K12">Permutations</a> 3 st <br/>( <font color="Maroon">l</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">q</font> &amp; <font color="Olive">q</font> <a href="matrix_2.html#NR1" target="_self">is_transposition</a>  )
 
<b>by </b><i><a class="txt" href="matrix_9.html#E5"><i><font color="Green">Lemma48</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
(  <a href="group_4.html#K3">Product</a> <font color="Maroon">l</font> <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> or  <a href="group_4.html#K3">Product</a> <font color="Maroon">l</font> <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> or  <a href="group_4.html#K3">Product</a> <font color="Maroon">l</font> <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#E4"><i><font color="Green">Lemma47</font></i></a>, </i>;<br/>


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