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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>;<br/>

<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E5">A1</font></i>: 
 <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conaffm.html#D3" target="_self" title="CONAFFM:def.3">CONAFFM:def 3</a><br/><b>let </b><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>





<b>assume </b><a NAME="E2:8"/><i><font color="Green" title="E6">A2</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:8"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E6:8"/><i><font color="Green" title="E8">A4</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">a'</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c8">b'</font> = <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c9">c'</font> = <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c10">e1'</font> = <font color="Maroon" title="c5">e1</font>, <font color="Maroon" title="c11">e2'</font> = <font color="Maroon" title="c6">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E8:8"/>
not <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c10">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c11">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" title="c7">a'</font>,<font color="Maroon" title="c10">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c11">e2'</font>
 ;<br/>

<a NAME="E2:8_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:8_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:8_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E6:8"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:8_1"/><b>then </b>
<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:8_1"/><b>then </b>
<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:8_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:8_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:8_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c12">d'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E10:8"/><i><font color="Green" title="E9">A5</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c10">e1'</font>,<font color="Maroon" title="c12">d'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c11">e2'</font>,<font color="Maroon" title="c12">d'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">d</font> = <font color="Maroon" title="c12">d'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c13">d</font>
;<br/>

<a NAME="E12:8"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:8"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:8"/><b>then </b><i><font color="Green" title="E10">A6</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:8"/><b>then </b><i><font color="Green" title="E11">A7</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E6:8"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E15:8"/><b>then </b><i><font color="Green" title="E12">A8</font></i>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E16:8"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:8"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:8"/><b>then </b><i><font color="Green" title="E13">A9</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:8"/><b>then </b><i><font color="Green" title="E14">A10</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E19:8"/><b>then </b><i><font color="Green" title="E15">A11</font></i>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E20:8"/><i><font color="Green" title="E16">A12</font></i>: 
 <a href="conaffm.html#NR6" title="CONAFFM:NR.6">LIN1_holds_in</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:8"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="conaffm.html#T3" target="_self" title="CONAFFM:th.3">Th3</a></i>;<br/>
<div><i><font color="Green" title="E17">A13</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" title="E18">A14</font></i>: 
<font color="Maroon" title="c13">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="E19">A15</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 ;<br/><a NAME="E2:8_2_1"/>
not <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">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" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font>
 ;<br/>

<a NAME="E2:8_2_1_1"/><b>then </b>
<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:8_2_1_1"/><b>then </b><i><font color="Green" title="E20">A16</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:8_2_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:8_2_1_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E3:8_2_1_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E6:8_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c14">o'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E4:8_2_1"/><i><font color="Green" title="E20">A17</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c14">o'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">o</font> = <font color="Maroon" title="c14">o'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">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" title="E21">A18</font></i>: 
<font color="Maroon" title="c13">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 ;<br/><a NAME="E2:8_2_1_2"/><i><font color="Green" title="E22">A19</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">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" title="E23">A20</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ;<br/>

<a NAME="E2:8_2_1_2_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:8_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:8_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:8_2_1_2_1"/><b>then </b><i><font color="Green" title="E24">A21</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E6:8_2_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_1"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:8_2_1_2_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:8_2_1_2_1"/><b>then </b><i><font color="Green" title="E25">A22</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:8_2_1_2_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 ;<br/>

<a NAME="E2:8_2_1_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:8_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:8_2_1_2_1"><i><font color="Green" title="E24">A21</font></i></a>, <a class="txt" href="conaffm.html#E8:8_2_1_2_1"><i><font color="Green" title="E25">A22</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E11:8_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E12:8_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E19:8"><i><font color="Green" title="E15">A11</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2"><i><font color="Green" title="E21">A18</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E13:8_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E14:8_2_1_2_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:8_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E16:8_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E17:8_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:8_2_1_2"/><i><font color="Green" title="E23">A23</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">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" title="E24">A24</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</font>
 ;<br/>

<a NAME="E2:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:8_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:8_2_1_2_2"/><b>then </b><i><font color="Green" title="E25">A25</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:8_2_1_2_2"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:8_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E18:8"><i><font color="Green" title="E14">A10</font></i></a>, <a class="txt" href="conaffm.html#E4:8_2_1_2_2"><i><font color="Green" title="E25">A25</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E10:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:8_2_1_2_2"/><b>then </b><i><font color="Green" title="E26">A26</font></i>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:8_2_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_2"><i><font color="Green" title="E24">A24</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E13:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:8_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:8_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:8_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="conaffm.html#E11:8_2_1_2_2"><i><font color="Green" title="E26">A26</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:8_2_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:8_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E19:8_2_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c16">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E5:8_2_1_2"/><i><font color="Green" title="E24">A27</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon" title="c17">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E7:8_2_1_2"/><i><font color="Green" title="E25">A28</font></i>: 
( <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font> &amp; <font color="Maroon" title="c13">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">e1'</font> = <font color="Maroon" title="c16">e1</font>, <font color="Maroon" title="c19">e2'</font> = <font color="Maroon" title="c17">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E9:8_2_1_2"/>
not <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c18">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c19">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" title="c7">a'</font>,<font color="Maroon" title="c18">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c19">e2'</font>
 ;<br/>

<a NAME="E2:8_2_1_2_3"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:8_2_1_2_3"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:8_2_1_2"><i><font color="Green" title="E24">A27</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:8_2_1_2_3"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E7:8_2_1_2"><i><font color="Green" title="E25">A28</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E5:8_2_1_2_3"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:8_2_1_2_3"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:8_2_1_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:8_2_1_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:8_2_1_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c20">d1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E11:8_2_1_2"/><i><font color="Green" title="E26">A29</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c18">e1'</font>,<font color="Maroon" title="c20">d1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c19">e2'</font>,<font color="Maroon" title="c20">d1'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">d1</font> = <font color="Maroon" title="c20">d1'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E13:8_2_1_2"/><i><font color="Green" title="E27">A30</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">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" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E11:8_2_1_2"><i><font color="Green" title="E26">A29</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_4"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:8_2_1_2_4"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:8_2_1_2"><i><font color="Green" title="E24">A27</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E4:8_2_1_2_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E14:8_2_1_2"/><i><font color="Green" title="E28">A31</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">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" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E11:8_2_1_2"><i><font color="Green" title="E26">A29</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_5"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_5"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E7:8_2_1_2"><i><font color="Green" title="E25">A28</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E15:8_2_1_2"/><i><font color="Green" title="E29">A32</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">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" title="E30">A33</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ;<br/>

<a NAME="E2:8_2_1_2_6"/><b>then </b><i><font color="Green" title="E31">A34</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="conaffm.html#E17:8"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:8_2_1_2_6"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:8_2_1_2_6"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_6"/><b>then </b><i><font color="Green" title="E32">A35</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:8_2_1_2"><i><font color="Green" title="E22">A19</font></i></a>, <a class="txt" href="conaffm.html#E2:8_2_1_2_6"><i><font color="Green" title="E31">A34</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:8_2_1_2_6"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:8_2_1_2_6"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_6"><i><font color="Green" title="E30">A33</font></i></a>, <a class="txt" href="conaffm.html#E5:8_2_1_2_6"><i><font color="Green" title="E32">A35</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E8:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E11:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:8_2_1_2_6"/><b>then </b><i><font color="Green" title="E33">A36</font></i>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:8_2_1_2_6"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E14:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:8_2_1_2_6"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:8_2_1_2_6"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E3:8_2_1_2"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="conaffm.html#E12:8_2_1_2_6"><i><font color="Green" title="E33">A36</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:8_2_1_2_6"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:8_2_1_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E20:8_2_1_2_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E16:8_2_1_2"/><i><font color="Green" title="E30">A37</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">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" title="E31">A38</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">d1</font>
 ;<br/>

<a NAME="E2:8_2_1_2_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:8_2_1_2_7"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_7"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:8_2_1_2_7"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8_2_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="txt" href="conaffm.html#E15:8_2_1_2"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_7"><i><font color="Green" title="E31">A38</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E10:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:8_2_1_2_7"/><b>then </b><i><font color="Green" title="E32">A39</font></i>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:8_2_1_2_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E13:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:8_2_1_2_7"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:8_2_1_2_7"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E3:8_2_1_2"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="conaffm.html#E11:8_2_1_2_7"><i><font color="Green" title="E32">A39</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:8_2_1_2_7"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:8_2_1_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E19:8_2_1_2_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:8_2_1_2"/><i><font color="Green" title="E31">A40</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 ;<br/>

<a NAME="E2:8_2_1_2_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_8"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E18:8_2_1_2"/><i><font color="Green" title="E32">A41</font></i>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="E33">A42</font></i>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_9"/><i><font color="Green" title="E34">A43</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_9_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:8_2_1_2_9"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8_2_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_9"><i><font color="Green" title="E33">A42</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_9"/><b>then </b><i><font color="Green" title="E35">A44</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:8_2_1_2_9"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8_2_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_9"><i><font color="Green" title="E33">A42</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E19:8"><i><font color="Green" title="E15">A11</font></i></a>, <a class="txt" href="conaffm.html#E2:8_2_1_2_9"><i><font color="Green" title="E34">A43</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:8_2_1_2_9"/><b>then </b><i><font color="Green" title="E36">A45</font></i>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E9:8_2_1_2_9"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:8_2_1_2_9"><i><font color="Green" title="E35">A44</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E10:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:8_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="conaffm.html#E8:8_2_1_2_9"><i><font color="Green" title="E36">A45</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E13:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E15:8"><i><font color="Green" title="E12">A8</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E14:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E15:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c12">d'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c12">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E18:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:8_2_1_2_9"/><b>then </b><i><font color="Green" title="E37">A46</font></i>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:8_2_1_2_9"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8_2_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1_2_9"><i><font color="Green" title="E33">A42</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E21:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:8_2"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="conaffm.html#E19:8_2_1_2_9"><i><font color="Green" title="E37">A46</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E22:8_2_1_2_9"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E23:8_2_1_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E24:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:8_2_1_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E26:8_2_1_2_9"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:8_2_1_2"/><i><font color="Green" title="E33">A47</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">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" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E2:8_2_1_2_10"/><b>then </b>
<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c14">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:8_2_1_2_10"/><b>then </b>
<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c12">d'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:8_2_1_2_10"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:8_2_1_2_10"/><b>then </b><i><font color="Green" title="E34">A48</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:8_2_1_2_10"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:8_2_1_2_10"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:8_2_1_2_10"/><b>then </b><i><font color="Green" title="E35">A49</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E9:8_2_1_2_10"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:8_2_1_2_10"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:8_2_1_2_10"><i><font color="Green" title="E34">A48</font></i></a>, <a class="txt" href="conaffm.html#E8:8_2_1_2_10"><i><font color="Green" title="E35">A49</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E20:8_2_1_2"/><i><font color="Green" title="E34">A50</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">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" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_11"/><b>then </b><i><font color="Green" title="E35">A51</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:8_2_1_2_11"/><i><font color="Green" title="E36">A52</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:8_2_1_2_11"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E13:8_2_1_2"><i><font color="Green" title="E27">A30</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:8_2_1_2_11"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:8_2_1_2_11"><i><font color="Green" title="E35">A51</font></i></a>, <a class="txt" href="conaffm.html#E3:8_2_1_2_11"><i><font color="Green" title="E36">A52</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:8_2_1_2_11"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:8_2_1_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c20">d1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:8_2_1_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c20">d1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:8_2_1_2_11"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:8_2_1_2_11"/><b>then </b><i><font color="Green" title="E37">A53</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:8_2_1_2_11"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:8_2_1_2_11"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:8_2_1_2_11"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E14:8_2_1_2_11"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:8_2_1_2"><i><font color="Green" title="E22">A19</font></i></a>, <a class="txt" href="conaffm.html#E10:8_2_1_2_11"><i><font color="Green" title="E37">A53</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:8_2_1_2_11"/><b>then </b><i><font color="Green" title="E38">A54</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E3:8_2_1_2_11"><i><font color="Green" title="E36">A52</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E16:8_2_1_2_11"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E17:8_2_1_2_11"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:8_2_1_2_11"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:8_2_1_2_11"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E20:8_2_1_2_11"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="txt" href="conaffm.html#E15:8_2_1_2_11"><i><font color="Green" title="E38">A54</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E21:8_2_1_2"/><i><font color="Green" title="E35">A55</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">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" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E2:8_2_1_2_12"/><b>then </b>
<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:8_2_1_2_12"/><b>then </b>
<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:8_2_1_2_12"/><b>then </b><i><font color="Green" title="E36">A56</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:8_2_1_2_12"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">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" title="E37">A57</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E4:8_2_1_2_12"><i><font color="Green" title="E36">A56</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:8_2_1_2_12"/>
<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c14">o'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:8_2_1_2_12"/><b>then </b>
<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c12">d'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c8">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E9:8_2_1_2_12"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E10:8_2_1_2_12"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:8_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="txt" href="conaffm.html#E6:8_2_1_2_12"><i><font color="Green" title="E37">A57</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:8_2_1_2"/><i><font color="Green" title="E36">A58</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">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" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font>
 ;<br/>

<a NAME="E2:8_2_1_2_13"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:8_2_1_2_13"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E16:8_2_1_2"><i><font color="Green" title="E30">A37</font></i></a>, <a class="txt" href="conaffm.html#E20:8_2_1_2"><i><font color="Green" title="E34">A50</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">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#E15:8_2_1_2"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div><a NAME="E23:8_2_1_2"/><i><font color="Green" title="E37">A59</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c4">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" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c20">d1'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E13:8_2_1_2"><i><font color="Green" title="E27">A30</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:8_2_1_2_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c20">d1'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:8_2_1_2_14"/><b>then </b>
<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c20">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:8_2_1_2_14"/><b>then </b>
<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c20">d1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:8_2_1_2_14"/><b>then </b><i><font color="Green" title="E38">A60</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:8_2_1_2_14"/><i><font color="Green" title="E39">A61</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_14_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:8_2_1_2_14"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c14">o'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:8_2_1_2_14"/><b>then </b>
<font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c7">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:8_2_1_2_14"/><b>then </b>
<font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c9">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c14">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E10:8_2_1_2_14"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:8_2_1_2_14"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:8_2_1_2_14"><i><font color="Green" title="E38">A60</font></i></a>, <a class="txt" href="conaffm.html#E6:8_2_1_2_14"><i><font color="Green" title="E39">A61</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:8_2_1_2_14"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:8_2_1_2_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">c'</font>,<font color="Maroon" title="c20">d1'</font>,<font color="Maroon" title="c14">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:8_2_1_2_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c20">d1'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:8_2_1_2_14"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E24:8_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">o'</font>,<font color="Maroon" title="c12">d'</font>,<font color="Maroon" title="c8">b'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:8_2_1"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E25:8_2_1_2"/><b>then </b><i><font color="Green" title="E38">A62</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E26:8_2_1_2"/><i><font color="Green" title="E39">A63</font></i>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E14:8_2_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E27:8_2_1_2"/>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">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" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">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" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/>

<a NAME="E2:8_2_1_2_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">a'</font>,<font color="Maroon" title="c8">b'</font>,<font color="Maroon" title="c9">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">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="txt" href="conaffm.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:8_2_1_2_15"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c21">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E18:8"><i><font color="Green" title="E14">A10</font></i></a>, <a class="txt" href="conaffm.html#E14:8_2_1_2"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E3:8_2_1_2_15"/>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>


</div><b>end;</b></div><a NAME="E28:8_2_1_2"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c13">d</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E20:8"><i><font color="Green" title="E16">A12</font></i></a>, <a class="txt" href="conaffm.html#E2:8_2_1_2"><i><font color="Green" title="E22">A19</font></i></a>, <a class="txt" href="conaffm.html#E3:8_2_1_2"><i><font color="Green" title="E23">A23</font></i></a>, <a class="txt" href="conaffm.html#E15:8_2_1_2"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="conaffm.html#E16:8_2_1_2"><i><font color="Green" title="E30">A37</font></i></a>, <a class="txt" href="conaffm.html#E17:8_2_1_2"><i><font color="Green" title="E31">A40</font></i></a>, <a class="txt" href="conaffm.html#E18:8_2_1_2"><i><font color="Green" title="E32">A41</font></i></a>, <a class="txt" href="conaffm.html#E19:8_2_1_2"><i><font color="Green" title="E33">A47</font></i></a>, <a class="txt" href="conaffm.html#E20:8_2_1_2"><i><font color="Green" title="E34">A50</font></i></a>, <a class="txt" href="conaffm.html#E21:8_2_1_2"><i><font color="Green" title="E35">A55</font></i></a>, <a class="txt" href="conaffm.html#E22:8_2_1_2"><i><font color="Green" title="E36">A58</font></i></a>, <a class="txt" href="conaffm.html#E23:8_2_1_2"><i><font color="Green" title="E37">A59</font></i></a>, <a class="txt" href="conaffm.html#E25:8_2_1_2"><i><font color="Green" title="E38">A62</font></i></a>, <a class="txt" href="conaffm.html#E26:8_2_1_2"><i><font color="Green" title="E39">A63</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></i>;<br/><b>hence </b><a NAME="E29:8_2_1_2"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E18:8"><i><font color="Green" title="E14">A10</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:8_2_1"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E4:8"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E17:8"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:8_2"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:8"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="conaffm.html#E13:8"><i><font color="Green" title="E10">A6</font></i></a>, <a class="txt" href="conaffm.html#E18:8"><i><font color="Green" title="E14">A10</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">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" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 ;<br/><a NAME="E2:8_3"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>hence </b><a NAME="E3:8_3"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E14:8"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E18:8"><i><font color="Green" title="E14">A10</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E23:8"/>
( <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E21:8"><i><font color="Green" title="E17">A13</font></i></a></i>;<br/>


</div>
