<?xml version="1.0"?>
<div class="add">

<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">K</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">perm2</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> holds   <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Olive" title="b3">perm2</font>,<font color="Olive" title="b1">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font><br/>  for <font color="Olive" title="b2">perm2</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> holds   <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Olive" title="b2">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b1">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font>; <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">perm2</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> holds   <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Olive" title="b1">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">perm2</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">  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span><br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_1"/>
( ( <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp; <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  ) or (  not <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp; <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  ) or ( <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp;  not <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  ) or (  not <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp;  not <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_1_1"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
( <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp; <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span><br/><div class="add"><a NAME="E2:35_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A2</font></span>: 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#D13" title="MATRIX_2:def.13">MATRIX_2:def 13</a></span>;<br/><a NAME="E3:35_1_1"/>
 <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="ref" href="matrix11.html#T23" target="_self" title="MATRIX11:th.23">Th23</a></span>;<br/><span class="kw">hence </span><a NAME="E4:35_1_1"/>
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_1"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="vectsp_1.html#D4" title="VECTSP_1:def.4">VECTSP_1:def 4</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_1_2"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
(  not <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp; <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span><br/><div class="add"><a NAME="E2:35_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A4</font></span>: 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#D13" title="MATRIX_2:def.13">MATRIX_2:def 13</a></span>;<br/><a NAME="E3:35_1_2"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</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"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T8" title="VECTSP_1:th.8">VECTSP_1:8</a></span>;<br/><a NAME="E4:35_1_2"/>
 <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">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="c2">K</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_2"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="matrix11.html#T23" target="_self" title="MATRIX11:th.23">Th23</a></span>;<br/><span class="kw">hence </span><a NAME="E5:35_1_2"/>
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_2"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E3:35_1_2"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="ref" href="vectsp_1.html#D4" title="VECTSP_1:def.4">VECTSP_1:def 4</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_3"><span class="kw">suppose </span></a><a NAME="E1:35_1_3"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
( <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp;  not <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span><br/><div class="add"><a NAME="E2:35_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A7</font></span>: 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#D13" title="MATRIX_2:def.13">MATRIX_2:def 13</a></span>;<br/><a NAME="E3:35_1_3"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
(  <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font> or  <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">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="c2">K</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix11.html#T11" target="_self" title="MATRIX11:th.11">Th11</a></span>;<br/><a NAME="E4:35_1_3"/>
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">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="c2">K</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_3"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="ref" href="matrix11.html#T22" target="_self" title="MATRIX11:th.22">Th22</a></span>;<br/><span class="kw">hence </span><a NAME="E5:35_1_3"/>
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_3"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="txt" href="#E3:35_1_3"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="ref" href="vectsp_1.html#D4" title="VECTSP_1:def.4">VECTSP_1:def 4</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_4"><span class="kw">suppose </span></a><a NAME="E1:35_1_4"/><span class="lab"><font color="Green" title="E31">A9</font></span>: 
(  not <font color="Maroon" title="c4">perm2</font> is  <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>  &amp;  not <font color="Maroon" title="c2">K</font> is  <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">Fanoian</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span><br/><div class="add"><a NAME="E2:35_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A10</font></span>: 
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#D13" title="MATRIX_2:def.13">MATRIX_2:def 13</a></span>;<br/><a NAME="E3:35_1_4"/><span class="lab"><font color="Green" title="E33">A11</font></span>: 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</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"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T8" title="VECTSP_1:th.8">VECTSP_1:8</a></span>;<br/><a NAME="E4:35_1_4"/><span class="lab"><font color="Green" title="E34">A12</font></span>: 
(  <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font> or  <a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">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="c2">K</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix11.html#T11" target="_self" title="MATRIX11:th.11">Th11</a></span>;<br/><a NAME="E5:35_1_4"/>
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">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="c2">K</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_4"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="ref" href="matrix11.html#T22" target="_self" title="MATRIX11:th.22">Th22</a></span>;<br/><span class="kw">hence </span><a NAME="E6:35_1_4"/>
 <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">perm2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix11.html#K2" title="MATRIX11:func.2">sgn</a> (<font color="Maroon" title="c4">perm2</font>,<font color="Maroon" title="c2">K</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_4"><span class="lab"><font color="Green" title="E32">A10</font></span></a>, <a class="txt" href="#E3:35_1_4"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E4:35_1_4"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="ref" href="vectsp_1.html#D4" title="VECTSP_1:def.4">VECTSP_1:def 4</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
