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

<b>let </b><font color="Maroon">X</font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/>

<b>assume </b><a NAME="E1:8"/><i><font color="Green">E26</font></i>: 
 <a href="conaffm.html#NR5" target="_self">LIN_holds_in</a> <font color="Maroon">X</font>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conaffm.html#D3" target="_self">CONAFFM:def 3</a><br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E2:8"/><i><font color="Green">E27</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 ;<br/>

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:8"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E6:8"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">c'</font> = <font color="Maroon">c</font>, <font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</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">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E8:8"/>
not <font color="Maroon">a'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">e2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_1"/>
<font color="Maroon">a'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">e2'</font>
 ;<br/>

<a NAME="E2:8_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:8_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">e2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:8_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:8_1"/><b>then </b>
<font color="Maroon">a'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:8_1"/><b>then </b>
<font color="Maroon">c'</font>,<font color="Maroon">a'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:8_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:8_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:8_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">d'</font> being   <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">X</font></span>)</span><b> such that </b><br/><a NAME="E10:8"/><i><font color="Green">E30</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">e1'</font>,<font color="Maroon">d'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">e2'</font>,<font color="Maroon">d'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon">d</font> = <font color="Maroon">d'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>take </b>
<font color="Maroon">d</font>
;<br/>

<a NAME="E12:8"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">e2</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:8"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:8"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E15:8"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E16:8"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">e1</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:8"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:8"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E19:8"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E20:8"/><i><font color="Green">E47</font></i>: 
 <a href="conaffm.html#NR6" target="_self">LIN1_holds_in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_2_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><a NAME="E2:8_2_1"/>
not <font color="Maroon">b'</font>,<font color="Maroon">d'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_1"/>
<font color="Maroon">b'</font>,<font color="Maroon">d'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font>
 ;<br/>

<a NAME="E2:8_2_1_1"/><b>then </b>
<font color="Maroon">a'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:8_2_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:8_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:8_2_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E6:8_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">o'</font> being   <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">X</font></span>)</span><b> such that </b><br/><a NAME="E4:8_2_1"/><i><font color="Green">E52</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">d'</font>,<font color="Maroon">o'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font>,<font color="Maroon">o'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">o</font> = <font color="Maroon">o'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_2_1_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E2:8_2_1_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:8_2_1_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:8_2_1_2_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:8_2_1_2_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:8_2_1_2_1"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E6:8_2_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">d'</font>
 
<b>by </b><i>, <a class="ref" href="conaffm.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:8_2_1_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:8_2_1_2_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:8_2_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:8_2_1_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:8_2_1_2_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="conaffm.html#D5" target="_self">Def5</a>, <a class="ref" href="conaffm.html#D6" target="_self">Def6</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E11:8_2_1_2_1"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E12:8_2_1_2_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E13:8_2_1_2_1"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E14:8_2_1_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:8_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E16:8_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E17:8_2_1_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:8_2_1_2"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:8_2_1_2_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:8_2_1_2_2"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:8_2_1_2_2"/>
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_2_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:8_2_1_2_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="conaffm.html#D6" target="_self">Def6</a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">d'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">d'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:8_2_1_2_2"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:8_2_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">d'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="conaffm.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:8_2_1_2_2"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:8_2_1_2_2"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="txt" href="conaffm.html#E1:8"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E19:8_2_1_2_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E5:8_2_1_2"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:8_2_1_2"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</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">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E9:8_2_1_2"/>
not <font color="Maroon">a'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d'</font>,<font color="Maroon">e2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_3"/>
<font color="Maroon">a'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d'</font>,<font color="Maroon">e2'</font>
 ;<br/>

<a NAME="E2:8_2_1_2_3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:8_2_1_2_3"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="conaffm.html#D5" target="_self">Def5</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:8_2_1_2_3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="conaffm.html#D6" target="_self">Def6</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E5:8_2_1_2_3"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:8_2_1_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:8_2_1_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:8_2_1_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:8_2_1_2_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">d1'</font> being   <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">X</font></span>)</span><b> such that </b><br/><a NAME="E11:8_2_1_2"/><i><font color="Green">E64</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">e1'</font>,<font color="Maroon">d1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d'</font>,<font color="Maroon">e2'</font>,<font color="Maroon">d1'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">d1</font> = <font color="Maroon">d1'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E13:8_2_1_2"/><i><font color="Green">E65</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_4"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_4"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">e1</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:8"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_4"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:8_2_1_2_4"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="conaffm.html#D5" target="_self">Def5</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E4:8_2_1_2_4"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E14:8_2_1_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_5"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_5"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:8"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_5"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_5"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="ref" href="conaffm.html#D6" target="_self">Def6</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E15:8_2_1_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_6"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:8_2_1_2_6"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:8_2_1_2_6"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:8_2_1_2_6"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_6"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:8_2_1_2_6"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_6_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_6_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:8_2_1_2_6"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="txt" href="conaffm.html#E10:8"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E8:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">o'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:8_2_1_2_6"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:8_2_1_2_6"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:8_2_1_2_6"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:8_2_1_2_6"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="conaffm.html#D4" target="_self">Def4</a>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">b'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E20:8_2_1_2_6"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E16:8_2_1_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_7"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:8_2_1_2_7"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:8_2_1_2_7"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_7"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:8_2_1_2_7"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conaffm.html#E6:8"><i><font color="Green">E29</font></i></a>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:8_2_1_2_7"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:8_2_1_2_7"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:8_2_1_2_7"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:8_2_1_2_7"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="conaffm.html#D4" target="_self">Def4</a>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E19:8_2_1_2_7"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:8_2_1_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_8"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:8_2_1_2_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_8"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E18:8_2_1_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_9"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_9"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_9_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_9_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_9_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_9_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:8_2_1_2_9"/>
<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green">E28</font></i></a>, , <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_9"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">b'</font>,<font color="Maroon">d'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:8_2_1_2_9"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green">E28</font></i></a>, , <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:8_2_1_2_9"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:8_2_1_2_9"/><b>then </b><i><font color="Green">E80</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E9:8_2_1_2_9"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d'</font>,<font color="Maroon">c'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:8_2_1_2_9"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:8_2_1_2_9"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E13:8_2_1_2_9"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E14:8_2_1_2_9"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E15:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:8_2_1_2_9"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:8_2_1_2_9"/>
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green">E28</font></i></a>, , <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E21:8_2_1_2_9"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E22:8_2_1_2_9"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E23:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E24:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E26:8_2_1_2_9"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:8_2_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_10"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E2:8_2_1_2_10"/><b>then </b>
<font color="Maroon">d'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:8_2_1_2_10"/><b>then </b>
<font color="Maroon">b'</font>,<font color="Maroon">d'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:8_2_1_2_10"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:8_2_1_2_10"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:8_2_1_2_10"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:8_2_1_2_10"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:8_2_1_2_10"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">a</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="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E9:8_2_1_2_10"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_10_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_10_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_10_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:8_2_1_2_10"/>
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E20:8_2_1_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_11"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_11"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_11"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:8_2_1_2_11"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_11_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_11_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:8_2_1_2_11"/>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_11"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:8_2_1_2_11"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:8_2_1_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">o'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:8_2_1_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:8_2_1_2_11"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:8_2_1_2_11"/><b>then </b><i><font color="Green">E99</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:8_2_1_2_11"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:8_2_1_2_11"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:8_2_1_2_11"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E14:8_2_1_2_11"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:8_2_1_2_11"/><b>then </b><i><font color="Green">E100</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E16:8_2_1_2_11"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E17:8_2_1_2_11"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:8_2_1_2_11"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:8_2_1_2_11"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E20:8_2_1_2_11"/>
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E21:8_2_1_2"/><i><font color="Green">E101</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">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_12"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_12"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E2:8_2_1_2_12"/><b>then </b>
<font color="Maroon">c'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:8_2_1_2_12"/><b>then </b>
<font color="Maroon">a'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:8_2_1_2_12"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:8_2_1_2_12"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_12_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_12_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_12_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:8_2_1_2_12"/><b>then </b><i><font color="Green">E103</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:8_2_1_2_12"/>
<font color="Maroon">b'</font>,<font color="Maroon">d'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:8_2_1_2_12"/><b>then </b>
<font color="Maroon">b'</font>,<font color="Maroon">d'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:8_2_1_2_12"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E10:8_2_1_2_12"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:8_2_1_2"/><i><font color="Green">E104</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_13"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>,<font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:8_2_1_2_13"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:8_2_1_2_13"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:8"><i><font color="Green">E30</font></i></a>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:8_2_1_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E6:8"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div><a NAME="E23:8_2_1_2"/><i><font color="Green">E105</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>,<font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_14"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:8_2_1_2_14"/><b>then </b>
<font color="Maroon">c'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:8_2_1_2_14"/><b>then </b>
<font color="Maroon">a'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:8_2_1_2_14"/><b>then </b><i><font color="Green">E106</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:8_2_1_2_14"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_14_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_14_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_14_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:8_2_1_2_14"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E8:8_2_1_2_14"/><b>then </b>
<font color="Maroon">c'</font>,<font color="Maroon">a'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:8_2_1_2_14"/><b>then </b>
<font color="Maroon">a'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:8_2_1_2_14"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:8_2_1_2_14"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:8_2_1_2_14"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:8_2_1_2_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:8_2_1_2_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:8_2_1_2_14"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E24:8_2_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d'</font>,<font color="Maroon">b'</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E25:8_2_1_2"/><b>then </b><i><font color="Green">E108</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E26:8_2_1_2"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">d1</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E27:8_2_1_2"/>
<font color="Maroon">d1</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_15"><b>proof </b></a><div class="add">

<a NAME="E1:8_2_1_2_15"/>
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2_1_2_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2_1_2_15_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_15_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:8_2_1_2_15"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="txt" href="conaffm.html#E4:8"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_15"/>
<font color="Maroon">d1</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>


</div><b>end;</b></div><a NAME="E28:8_2_1_2"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 <b>by </b><i>, , <a class="ref" href="conaffm.html#D4" target="_self">Def4</a>, <a class="txt" href="conaffm.html#E6:8"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conaffm.html#E10:8"><i><font color="Green">E30</font></i></a>, , , , , , , , , , </i>;<br/><b>hence </b><a NAME="E29:8_2_1_2"/>
( <font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:8_2_1"/>
( <font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i>, , , <a class="ref" href="analmetr.html#T83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:8_2"/>
( <font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i>, , , <a class="ref" href="analmetr.html#T83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_3"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><a NAME="E2:8_3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>hence </b><a NAME="E3:8_3"/>
( <font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E23:8"/>
( <font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 <b>by </b><i/>;<br/>


</div>
