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

<b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> 2;<br/>

<a NAME="E1:1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">f</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> 2, <a href="finseq_1.html#K2">Seg</a> 2 &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2 )
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E2:1"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 
<b>by </b><i><a class="ref" href="funct_2.html#T67">FUNCT_2:67</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">p</font> = <font color="Maroon">f</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E4:1"/>
1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 2
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/>
<a NAME="E6:1"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E7:1"/><i><font color="Green">E43</font></i>: 
2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E8:1"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E9:1"/><i><font color="Green">E45</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:1"/><i><font color="Green">E46</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E11:1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 2
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/>
<a NAME="E12:1"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:1_1_1"/>
( ( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 1 ) or ( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 2 ) )
 </span><b>by </b><i>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1"><b>case </b></a><a NAME="E1:1_1_1_1"/>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 1 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:1_1_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_2"><b>case </b></a><a NAME="E1:1_1_1_2"/>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:1_1_1_2"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">1,2</span><a href="finseq_1.html#K10">*&gt;</a></span> or <font color="Maroon">f</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="finseq_1.html#T61">FINSEQ_1:61</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_3"><b>case </b></a><a NAME="E1:1_1_1_3"/>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 1 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:1_1_1_3"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">1,2</span><a href="finseq_1.html#K10">*&gt;</a></span> or <font color="Maroon">f</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="finseq_1.html#T61">FINSEQ_1:61</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_4"><b>case </b></a><a NAME="E1:1_1_1_4"/>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:1_1_1_4"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E14:1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default">1,2</span><a href="finseq_1.html#K10">*&gt;</a></span> or <font color="Maroon">f</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> )
 ;<br/>


</div>
