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

<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3;<br/>

<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E33">A1</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default">3,1,2</span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
 ;<br/>

<a NAME="E2:43"/><b>then </b><i><font color="Green" title="E34">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</a>, <a class="ref" href="finseq_3.html#T30" title="FINSEQ_3:th.30">FINSEQ_3:30</a></i>;<br/>
<a NAME="E3:43"/>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  holds <br/>(  not <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> or  not <font color="Olive" title="b2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> or  not <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">j</font> or  not <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">j</font> or  not <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font> or  ex <font color="Olive" title="b3">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b3">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b3">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> &amp; not <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><a NAME="E2:43_1"/><i><font color="Green" title="E35">A3</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c2">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">i</font> &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Olive" title="b1">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> holds <br/><font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> ) )
 ;<br/>

<a NAME="E3:43_1"/>
 ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Olive" title="b1">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:43_1_1"/><i><font color="Green" title="E36">A4</font></i>: 
( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) &amp; ( <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) )
 
<b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E2:43_1"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_1_1_1"/>
( ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) or ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) or ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) or ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) )
 </span><b>by </b><i><a class="txt" href="matrix_9.html#E2:43_1"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1"><i><font color="Green" title="E36">A4</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_1"><b>suppose </b></a><a NAME="E1:43_1_1_1_1"/><i><font color="Green" title="E37">A5</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ;<br/><div class="add"><b>take </b>
3
;<br/><b>thus </b><a NAME="E2:43_1_1_1_1"/>
( 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1_1_1"><i><font color="Green" title="E37">A5</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_2"><b>suppose </b></a><a NAME="E1:43_1_1_1_2"/><i><font color="Green" title="E37">A6</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 ;<br/><div class="add"><b>take </b>
1
;<br/><b>thus </b><a NAME="E2:43_1_1_1_2"/>
( 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1_1_2"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_3"><b>suppose </b></a><a NAME="E1:43_1_1_1_3"/><i><font color="Green" title="E37">A7</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 ;<br/><div class="add"><b>take </b>
2
;<br/><b>thus </b><a NAME="E2:43_1_1_1_3"/>
( 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1_1_3"><i><font color="Green" title="E37">A7</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_4"><b>suppose </b></a><a NAME="E1:43_1_1_1_4"/><i><font color="Green" title="E37">A8</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ;<br/><div class="add"><b>take </b>
3
;<br/><b>thus </b><a NAME="E2:43_1_1_1_4"/>
( 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1_1_4"><i><font color="Green" title="E37">A8</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_5"><b>suppose </b></a><a NAME="E1:43_1_1_1_5"/><i><font color="Green" title="E37">A9</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ;<br/><div class="add"><b>take </b>
2
;<br/><b>thus </b><a NAME="E2:43_1_1_1_5"/>
( 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1_1_5"><i><font color="Green" title="E37">A9</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1_1_6"><b>suppose </b></a><a NAME="E1:43_1_1_1_6"/><i><font color="Green" title="E37">A10</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ;<br/><div class="add"><b>take </b>
1
;<br/><b>thus </b><a NAME="E2:43_1_1_1_6"/>
( 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E1:43_1_1_1_6"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c4">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E5:43_1"/><i><font color="Green" title="E36">A11</font></i>: 
( <font color="Maroon" title="c4">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">i</font> &amp; <font color="Maroon" title="c4">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font> &amp; <font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">p</font> )
 ;<br/>
<a NAME="E6:43_1"/><i><font color="Green" title="E37">A12</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E2:43_1"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="matrix_9.html#E5:43_1"><i><font color="Green" title="E36">A11</font></i></a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:43_1_2"/>
( <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="matrix_9.html#E2:43"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="matrix_9.html#E5:43_1"><i><font color="Green" title="E36">A11</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_2_1"><b>suppose </b></a><a NAME="E1:43_1_2_1"/>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="matrix_9.html#E1:43"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="matrix_9.html#E6:43_1"><i><font color="Green" title="E37">A12</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_2_2"><b>suppose </b></a><a NAME="E1:43_1_2_2"/>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="matrix_9.html#E1:43"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="matrix_9.html#E6:43_1"><i><font color="Green" title="E37">A12</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_2_3"><b>suppose </b></a><a NAME="E1:43_1_2_3"/>
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><a NAME="E2:43_1_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="matrix_9.html#E1:43"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="matrix_9.html#E6:43_1"><i><font color="Green" title="E37">A12</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E4:43"/>
not <font color="Maroon" title="c1">p</font> <a href="matrix_2.html#NR1" title="MATRIX_2:NR.1">is_transposition</a> 
 <b>by </b><i><a class="ref" href="matrix_2.html#D14" title="MATRIX_2:def.14">MATRIX_2:def 14</a></i>;<br/>


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