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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">tr</font> be    <a href="matrix_2.html#M1" title="MATRIX_2:mode.1">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c2">tr</font> <a href="matrix_2.html#NR1" title="MATRIX_2:NR.1">is_transposition</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">K</font> being  <a href="vectsp_1.html#V9" title="VECTSP_1:attr.9">Fanoian</a> <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/>
<a NAME="E3:36"/>
 <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> <font color="Maroon" title="c2">tr</font>,<font color="Maroon" title="c3">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">K</font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrix11.html#E1:36"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="matrix11.html#T14" target="_self" title="MATRIX11:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E4:36"/>
not <font color="Maroon" title="c2">tr</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>
 <b>by </b><i><a class="ref" href="matrix11.html#T23" target="_self" title="MATRIX11:th.23">Th23</a></i>;<br/>


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