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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> 2</span>)</span>;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being    <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K11">Permutations</a> 2<b> such that </b><a NAME="E1:8"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="matrix_2.html#NR1" target="_self">is_transposition</a>  )
 ;<br/>

<a NAME="E2:8"/><i><font color="Green">E13</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13">Group_of_Perm</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_2.html#K11">Permutations</a> 2
 
<b>by </b><i><a class="ref" href="matrix_2.html#D13">MATRIX_2:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> 2 <b>by </b><i><a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a>, <a class="txt" href="matrix_7.html#E2:8"><i><font color="Green">E13</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:8"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="matrix_7.html#E1:8"><i><font color="Green">E12</font></i></a>, <a class="ref" href="matrix_2.html#D14">MATRIX_2:def 14</a></i>;<br/>
<a NAME="E6:8"/>
<font color="Maroon">c<sub>3</sub></font> <a href="matrix_2.html#NR1" target="_self">is_transposition</a> 
 
<b>by </b><i><a class="ref" href="matrix_2.html#D14">MATRIX_2:def 14</a>, <a class="txt" href="matrix_7.html#E1:8"><i><font color="Green">E12</font></i></a>, <a class="txt" href="matrix_7.html#E5:8"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">2,1</span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="matrix_7.html#T4" target="_self">Th4</a></i>;<br/>


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