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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">tr</font> being    <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>  st <font color="Olive" title="b1">tr</font> is  <a href="matrix_2.html#V4" title="MATRIX_2:attr.4">being_transposition</a>  holds <br/> not <font color="Olive" title="b1">tr</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">K</font> =  the   <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">tr</font> is  <a href="matrix_2.html#V4" title="MATRIX_2:attr.4">being_transposition</a>  implies  not <font color="Maroon" title="c3">tr</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:36"/>
<font color="Maroon" title="c3">tr</font> is  <a href="matrix_2.html#V4" title="MATRIX_2:attr.4">being_transposition</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c3">tr</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> </span><br/>

<a NAME="E2:36"/><span class="kw">then </span>
 <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c3">tr</font>, the   <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>) <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>  the   <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix11.html#T14" target="_self" title="MATRIX11:th.14">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:36"/>
 not <font color="Maroon" title="c3">tr</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix11.html#T23" target="_self" title="MATRIX11:th.23">Th23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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