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

<b>let </b><font color="Maroon">MS</font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">c1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green">E34</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> )
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font>
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a2</font> )
 <b>and </b><br/><a NAME="E4:26"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c1</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c1</font>,<font color="Maroon">a2</font> )
 ;<br/>

<b>assume </b><a NAME="E5:26"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font>
 ;<br/>

<a NAME="E6:26"/>
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 
<b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self">Def5</a>, </i>;<br/>
<a NAME="E7:26"/><b>then </b><i><font color="Green">E64</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a2</font> &amp; <font color="Maroon">c1</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">a2</font> )
 
<b>by </b><i><a class="ref" href="euclmetr.html#D7" target="_self">Def7</a>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<b>reconsider </b><font color="Maroon">o'</font> = <font color="Maroon">o</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">a2'</font> = <font color="Maroon">a2</font>, <font color="Maroon">c1'</font> = <font color="Maroon">c1</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">MS</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E9:26"/>
( <font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font> &amp; <font color="Maroon">c1'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1'</font>,<font color="Maroon">a2'</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:26"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a2'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c1'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:26"/><b>then </b><i><font color="Green">E66</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">o'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">c1'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E12:26"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">a1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">a2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E13:26"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c1'</font>,<font color="Maroon">a1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c1'</font>,<font color="Maroon">a2'</font> )
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E14:26"/><b>then </b>
( <font color="Maroon">o'</font>,<font color="Maroon">c1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font> &amp; <font color="Maroon">o'</font>,<font color="Maroon">c1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:26"/><b>then </b>
( <font color="Maroon">o</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a2</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:26"/><b>then </b><i><font color="Green">E67</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a2</font> )
 
<b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self">Def5</a>, <a class="ref" href="euclmetr.html#D6" target="_self">Def6</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E17:26"/>
( <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> or <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E18:26"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="euclmetr.html#D7" target="_self">Def7</a>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<b>hence </b><a NAME="E19:26"/>
contradiction
 <b>by </b><i><a class="ref" href="euclmetr.html#D5" target="_self">Def5</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div>
