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<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#T27" target="_self">Th27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>1</sub></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> as   <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></i>;<br/>
<a NAME="E3:57"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> 3</span>)</span> holds <br/>(  not <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="nat_1.html#K4">mod</a> 2 <a href="hidden.html#R1">=</a> 0 or  not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_4.html#K3">Product</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <font color="Olive">b<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being   <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K11">Permutations</a> 3 holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> or  not <font color="Olive">b<sub>3</sub></font> <a href="matrix_2.html#NR1" target="_self">is_transposition</a>  ) ) ) )
 
<b>by </b><i><a class="ref" href="matrix_9.html#T41" target="_self">Th41</a>, <a class="txt" href="matrix_9.html#E35"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:57"/>
<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="matrix_2.html#V3">odd</a> <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#D15">MATRIX_2:def 15</a></i>;<br/>


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