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

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

<a NAME="E1:22"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a>  implies <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a> 
 ;<br/>

<a NAME="E2:22_1"/><b>then </b><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T25" title="AFF_2:th.25">AFF_2:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c6">a4</font>, <font color="Maroon" title="c7">b1</font>, <font color="Maroon" title="c8">b2</font>, <font color="Maroon" title="c9">b3</font>, <font color="Maroon" title="c10">b4</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>let </b><font color="Maroon" title="c11">M</font>, <font color="Maroon" title="c12">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>assume </b><a NAME="E1:22_1_1"/><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c11">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c12">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> )
 ;<br/><a NAME="E2:22_1_1"/><b>then </b><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c11">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c12">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">N</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><div><i><font color="Green" title="E20">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_1"/><i><font color="Green" title="E21">A7</font></i>: 
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a4</font> )
 ;<br/><a NAME="E2:22_1_1_1"/><i><font color="Green" title="E22">A8</font></i>: 
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_1"/><i><font color="Green" title="E23">A9</font></i>: 
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 ;<br/>

<a NAME="E2:22_1_1_1_1"/><i><font color="Green" title="E24">A10</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:22_1_1_1_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:22_1_1_1_1"/><b>then </b><i><font color="Green" title="E25">A11</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</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="E5:22_1_1_1_1"/>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E6:22_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E7:22_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="conmetr1.html#E4:22_1_1_1_1"><i><font color="Green" title="E25">A11</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:22_1_1_1"/>
 ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_2"/><i><font color="Green" title="E23">A12</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  holds <br/>(  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> or  not <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> or  not <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> or  not <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> )
 ;<br/>

<a NAME="E2:22_1_1_1_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:22_1_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</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/>
<b>hence </b><a NAME="E4:22_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1_2"><i><font color="Green" title="E23">A12</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c13">d</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="E5:22_1_1_1"/><i><font color="Green" title="E23">A13</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="translac.html#T2" title="TRANSLAC:th.2">TRANSLAC:2</a></i>;<br/><a NAME="E6:22_1_1_1"/><i><font color="Green" title="E24">A14</font></i>: 
<font color="Maroon" title="c2">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="22_1_1_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_3"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ;<br/>

<a NAME="E2:22_1_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</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="E3:22_1_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:22_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c13">d</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>then consider </b><font color="Maroon" title="c14">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E9:22_1_1_1"/><i><font color="Green" title="E25">A15</font></i>: 
( <font color="Maroon" title="c14">Y</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E10:22_1_1_1"/>
 ex <font color="Olive" title="b1">d1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Olive" title="b1">d1</font> &amp; <font color="Olive" title="b1">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_4"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c15">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="E2:22_1_1_1_4"/><i><font color="Green" title="E26">A16</font></i>: 
( <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">e1</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c16">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="E4:22_1_1_1_4"/><i><font color="Green" title="E27">A17</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">e2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:22_1_1_1_4"/>
not <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_4_1"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">e2</font>
 ;<br/>

<a NAME="E2:22_1_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1_1_1_4"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:22_1_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:22_1_1_1_4"><i><font color="Green" title="E27">A17</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:22_1_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">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="E5:22_1_1_1_4_1"/><b>then </b><i><font color="Green" title="E28">A18</font></i>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:22_1_1_1_4_1"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</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="E7:22_1_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E5:22_1_1_1_4_1"><i><font color="Green" title="E28">A18</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:22_1_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</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="E9:22_1_1_1_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</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="E10:22_1_1_1_4_1"/><b>then </b><i><font color="Green" title="E29">A19</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">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="E11:22_1_1_1_4_1"/><i><font color="Green" title="E30">A20</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E12:22_1_1_1_4_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E13:22_1_1_1_4_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</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/>
<b>hence </b><a NAME="E14:22_1_1_1_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="conmetr1.html#E10:22_1_1_1_4_1"><i><font color="Green" title="E29">A19</font></i></a>, <a class="txt" href="conmetr1.html#E11:22_1_1_1_4_1"><i><font color="Green" title="E30">A20</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c17">d1</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="E7:22_1_1_1_4"/><i><font color="Green" title="E28">A21</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">e1</font>,<font color="Maroon" title="c17">d1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">e2</font>,<font color="Maroon" title="c17">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>take </b>
<font color="Maroon" title="c17">d1</font>
;<br/>

<a NAME="E8:22_1_1_1_4"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c16">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c17">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:22_1_1_1_4"><i><font color="Green" title="E28">A21</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="E9:22_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c17">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:22_1_1_1_4"><i><font color="Green" title="E27">A17</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:22_1_1_1_4"/><b>then </b><i><font color="Green" title="E29">A22</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c17">d1</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="E11:22_1_1_1_4"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:22_1_1_1_4"><i><font color="Green" title="E28">A21</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="E12:22_1_1_1_4"/><b>then </b>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1_1_1_4"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E13:22_1_1_1_4"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c17">d1</font> &amp; <font color="Maroon" title="c17">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E6:22_1_1_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="conmetr1.html#E9:22_1_1_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr1.html#E10:22_1_1_1_4"><i><font color="Green" title="E29">A22</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c15">d1</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="E12:22_1_1_1"/><i><font color="Green" title="E26">A23</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp; <font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 ;<br/><a NAME="E13:22_1_1_1"/>
 ex <font color="Olive" title="b1">c1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Olive" title="b1">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_5"><b>proof </b></a><div class="add">

<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="E2:22_1_1_1_5"/><i><font color="Green" title="E27">A24</font></i>: 
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">e1</font> &amp; <font color="Maroon" title="c8">b2</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="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</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="E4:22_1_1_1_5"/><i><font color="Green" title="E28">A25</font></i>: 
( <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c17">e2</font> &amp; <font color="Maroon" title="c4">a2</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="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:22_1_1_1_5"/>
not <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c17">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_5_1"/>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c17">e2</font>
 ;<br/>

<a NAME="E2:22_1_1_1_5_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c17">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1_1_1_5"><i><font color="Green" title="E27">A24</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:22_1_1_1_5_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:22_1_1_1_5"><i><font color="Green" title="E28">A25</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:22_1_1_1_5_1"/><b>then </b>
<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</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="E5:22_1_1_1_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</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/>
<b>hence </b><a NAME="E6:22_1_1_1_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c18">c1</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="E7:22_1_1_1_5"/><i><font color="Green" title="E29">A26</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">e1</font>,<font color="Maroon" title="c18">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c17">e2</font>,<font color="Maroon" title="c18">c1</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>take </b>
<font color="Maroon" title="c18">c1</font>
;<br/>

<a NAME="E8:22_1_1_1_5"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c17">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c18">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:22_1_1_1_5"><i><font color="Green" title="E29">A26</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="E9:22_1_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c18">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:22_1_1_1_5"><i><font color="Green" title="E28">A25</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:22_1_1_1_5"/><b>then </b><i><font color="Green" title="E30">A27</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c18">c1</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="E11:22_1_1_1_5"/>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c18">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:22_1_1_1_5"><i><font color="Green" title="E29">A26</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E12:22_1_1_1_5"/>
( <font color="Maroon" title="c18">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c18">c1</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_5"><i><font color="Green" title="E27">A24</font></i></a>, <a class="txt" href="conmetr1.html#E10:22_1_1_1_5"><i><font color="Green" title="E30">A27</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c16">c1</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="E15:22_1_1_1"/><i><font color="Green" title="E27">A28</font></i>: 
( <font color="Maroon" title="c16">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">c1</font> )
 ;<br/><a NAME="E16:22_1_1_1"/>
 ex <font color="Olive" title="b1">c2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b1">c2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_6"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c17">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="E2:22_1_1_1_6"/><i><font color="Green" title="E28">A29</font></i>: 
( <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">e1</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c18">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="E4:22_1_1_1_6"/><i><font color="Green" title="E29">A30</font></i>: 
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c18">e2</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:22_1_1_1_6"/>
not <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c18">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_6_1"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c18">e2</font>
 ;<br/>

<a NAME="E2:22_1_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c18">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1_1_1_6"><i><font color="Green" title="E28">A29</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:22_1_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:22_1_1_1_6"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:22_1_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</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="E5:22_1_1_1_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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/>
<b>hence </b><a NAME="E6:22_1_1_1_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c19">c2</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="E7:22_1_1_1_6"/><i><font color="Green" title="E30">A31</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">e1</font>,<font color="Maroon" title="c19">c2</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c18">e2</font>,<font color="Maroon" title="c19">c2</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>take </b>
<font color="Maroon" title="c19">c2</font>
;<br/>

<a NAME="E8:22_1_1_1_6"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c18">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c19">c2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:22_1_1_1_6"><i><font color="Green" title="E30">A31</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="E9:22_1_1_1_6"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c19">c2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:22_1_1_1_6"><i><font color="Green" title="E29">A30</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:22_1_1_1_6"/><b>then </b><i><font color="Green" title="E31">A32</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c19">c2</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="E11:22_1_1_1_6"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c19">c2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:22_1_1_1_6"><i><font color="Green" title="E30">A31</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E12:22_1_1_1_6"/>
( <font color="Maroon" title="c19">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c19">c2</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_6"><i><font color="Green" title="E28">A29</font></i></a>, <a class="txt" href="conmetr1.html#E10:22_1_1_1_6"><i><font color="Green" title="E31">A32</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c17">c2</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="E18:22_1_1_1"/><i><font color="Green" title="E28">A33</font></i>: 
( <font color="Maroon" title="c17">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c17">c2</font> )
 ;<br/><a NAME="E19:22_1_1_1"/><i><font color="Green" title="E29">A34</font></i>: 
( <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_7"/><i><font color="Green" title="E30">A35</font></i>: 
(  not <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">N</font> or  not <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> or  not <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> )
 ;<br/>

<div><i><font color="Green" title="E31">A36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_7_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_1_7_1"/><i><font color="Green" title="E32">A37</font></i>: 
<font color="Maroon" title="c11">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y</font>
 ;<br/><a NAME="E2:22_1_1_1_7_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</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="E3:22_1_1_1_7_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="conmetr1.html#E9:22_1_1_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1_7_1"><i><font color="Green" title="E32">A37</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_7_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_1_7_2"/><i><font color="Green" title="E32">A38</font></i>: 
<font color="Maroon" title="c12">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y</font>
 ;<br/><a NAME="E2:22_1_1_1_7_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</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="E3:22_1_1_1_7_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="conmetr1.html#E9:22_1_1_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1_7_2"><i><font color="Green" title="E32">A38</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1_1_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1_7"><i><font color="Green" title="E30">A35</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_7"><i><font color="Green" title="E31">A36</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E20:22_1_1_1"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_8"><b>proof </b></a><div class="add">

<a NAME="E1:22_1_1_1_8"/><i><font color="Green" title="E30">A39</font></i>: 
( <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="conmetr1.html#E12:22_1_1_1"><i><font color="Green" title="E26">A23</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="E2:22_1_1_1_8"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">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="E3:22_1_1_1_8"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:22_1_1_1_8"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1_8"><i><font color="Green" title="E30">A39</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E21:22_1_1_1"/><b>then </b><i><font color="Green" title="E30">A40</font></i>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d1</font>,<font color="Maroon" title="c17">c2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E6:22_1_1_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="conmetr1.html#E9:22_1_1_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr1.html#E12:22_1_1_1"><i><font color="Green" title="E26">A23</font></i></a>, <a class="txt" href="conmetr1.html#E18:22_1_1_1"><i><font color="Green" title="E28">A33</font></i></a>, <a class="txt" href="conmetr1.html#E19:22_1_1_1"><i><font color="Green" title="E29">A34</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>;<br/><a NAME="E22:22_1_1_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_9"><b>proof </b></a><div class="add">

<a NAME="E1:22_1_1_1_9"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E5:22_1_1_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="txt" href="conmetr1.html#E12:22_1_1_1"><i><font color="Green" title="E26">A23</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E2:22_1_1_1_9"/><b>then </b><i><font color="Green" title="E31">A41</font></i>: 
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</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="E3:22_1_1_1_9"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">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="E4:22_1_1_1_9"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E5:22_1_1_1_9"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_9"><i><font color="Green" title="E31">A41</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E23:22_1_1_1"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d1</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E6:22_1_1_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="conmetr1.html#E9:22_1_1_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr1.html#E12:22_1_1_1"><i><font color="Green" title="E26">A23</font></i></a>, <a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="txt" href="conmetr1.html#E19:22_1_1_1"><i><font color="Green" title="E29">A34</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>;<br/><a NAME="E24:22_1_1_1"/><b>then </b><i><font color="Green" title="E31">A42</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c2</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:22_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E6:22_1_1_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="conmetr1.html#E9:22_1_1_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="conmetr1.html#E12:22_1_1_1"><i><font color="Green" title="E26">A23</font></i></a>, <a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="txt" href="conmetr1.html#E18:22_1_1_1"><i><font color="Green" title="E28">A33</font></i></a>, <a class="txt" href="conmetr1.html#E19:22_1_1_1"><i><font color="Green" title="E29">A34</font></i></a>, <a class="txt" href="conmetr1.html#E21:22_1_1_1"><i><font color="Green" title="E30">A40</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>;<br/><a NAME="E25:22_1_1_1"/><i><font color="Green" title="E32">A43</font></i>: 
<font color="Maroon" title="c16">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_10"/>
<font color="Maroon" title="c16">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">c2</font>
 ;<br/>

<a NAME="E2:22_1_1_1_10"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c16">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E18:22_1_1_1"><i><font color="Green" title="E28">A33</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:22_1_1_1_10"/><b>then </b><i><font color="Green" title="E33">A44</font></i>: 
<font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c16">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:22_1_1_1_10"/><i><font color="Green" title="E34">A45</font></i>: 
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_10_1"/>
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">c1</font>
 ;<br/>

<a NAME="E2:22_1_1_1_10_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:22_1_1_1_10_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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="E4:22_1_1_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c4">a2</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="E5:22_1_1_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</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="E6:22_1_1_1_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:22_1_1_1_10"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c16">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c7">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:22_1_1_1_10"/><b>then </b>
<font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:22_1_1_1_10"><i><font color="Green" title="E33">A44</font></i></a>, <a class="txt" href="conmetr1.html#E4:22_1_1_1_10"><i><font color="Green" title="E34">A45</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:22_1_1_1_10"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</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/>
<b>hence </b><a NAME="E8:22_1_1_1_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E26:22_1_1_1"/><i><font color="Green" title="E33">A46</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1_1_11"/><i><font color="Green" title="E34">A47</font></i>: 
(  not <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c1</font> or  not <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c2</font> )
 ;<br/>

<div><i><font color="Green" title="E35">A48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_11_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_1_11_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">c1</font>
 ;<br/><a NAME="E2:22_1_1_1_11_1"/><b>then </b><i><font color="Green" title="E36">A49</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E3:22_1_1_1_11_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:22_1_1_1_11_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_11_1"><i><font color="Green" title="E36">A49</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E5:22_1_1_1_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</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/><b>hence </b><a NAME="E6:22_1_1_1_11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_11_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_1_11_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">c2</font>
 ;<br/><a NAME="E2:22_1_1_1_11_2"/><b>then </b><i><font color="Green" title="E36">A50</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E18:22_1_1_1"><i><font color="Green" title="E28">A33</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E3:22_1_1_1_11_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:22_1_1_1_11_2"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_11_2"><i><font color="Green" title="E36">A50</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E5:22_1_1_1_11_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c5">a3</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/><b>hence </b><a NAME="E6:22_1_1_1_11_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1_1_1_11"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1_1_11"><i><font color="Green" title="E34">A47</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_1_11"><i><font color="Green" title="E35">A48</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E27:22_1_1_1"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E28:22_1_1_1"/><b>then </b><i><font color="Green" title="E34">A51</font></i>: 
<font color="Maroon" title="c10">b4</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c16">c1</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="E29:22_1_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c2</font>,<font color="Maroon" title="c7">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E18:22_1_1_1"><i><font color="Green" title="E28">A33</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E30:22_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c2</font>,<font color="Maroon" title="c7">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E31:22_1_1_1"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c2</font>,<font color="Maroon" title="c7">b1</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="E32:22_1_1_1"/><b>then </b>
<font color="Maroon" title="c10">b4</font>,<font color="Maroon" title="c9">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c2</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E15:22_1_1_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="txt" href="conmetr1.html#E18:22_1_1_1"><i><font color="Green" title="E28">A33</font></i></a>, <a class="txt" href="conmetr1.html#E26:22_1_1_1"><i><font color="Green" title="E33">A46</font></i></a>, <a class="txt" href="conmetr1.html#E28:22_1_1_1"><i><font color="Green" title="E34">A51</font></i></a>, <a class="ref" href="aff_2.html#D2" title="AFF_2:def.2">AFF_2:def 2</a></i>;<br/><a NAME="E33:22_1_1_1"/><b>then </b>
<font color="Maroon" title="c10">b4</font>,<font color="Maroon" title="c9">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E24:22_1_1_1"><i><font color="Green" title="E31">A42</font></i></a>, <a class="txt" href="conmetr1.html#E25:22_1_1_1"><i><font color="Green" title="E32">A43</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E34:22_1_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_2"/><i><font color="Green" title="E21">A52</font></i>: 
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font> or <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a4</font> )
 ;<br/><div><i><font color="Green" title="E22">A53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_2_1"/><i><font color="Green" title="E23">A54</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ;<br/><a NAME="E2:22_1_1_2_1"/><i><font color="Green" title="E24">A55</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:22_1_1_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:22_1_1_2_1"/><b>then </b><i><font color="Green" title="E25">A56</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</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="E5:22_1_1_2_1"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_2_1"><i><font color="Green" title="E23">A54</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E6:22_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E7:22_1_1_2_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_2_1"><i><font color="Green" title="E23">A54</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_2_1"><i><font color="Green" title="E24">A55</font></i></a>, <a class="txt" href="conmetr1.html#E4:22_1_1_2_1"><i><font color="Green" title="E25">A56</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_2_2"/><i><font color="Green" title="E23">A57</font></i>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a4</font>
 ;<br/><a NAME="E2:22_1_1_2_2"/><i><font color="Green" title="E24">A58</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:22_1_1_2_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:22_1_1_2_2"/><b>then </b><i><font color="Green" title="E25">A59</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c10">b4</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="E5:22_1_1_2_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_2_2"><i><font color="Green" title="E23">A57</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E6:22_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E7:22_1_1_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_1_1_2_2"><i><font color="Green" title="E23">A57</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_2_2"><i><font color="Green" title="E24">A58</font></i></a>, <a class="txt" href="conmetr1.html#E4:22_1_1_2_2"><i><font color="Green" title="E25">A59</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:22_1_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_1_1_2"><i><font color="Green" title="E21">A52</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_1_1_2"><i><font color="Green" title="E22">A53</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:22_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:22_1_1"><i><font color="Green" title="E20">A6</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1"/>
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a> 
 <b>by </b><i><a class="ref" href="conmetr1.html#D6" target="_self" title="CONMETR1:def.6">Def6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:22"/>
( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a>  implies <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_2"/><i><font color="Green" title="E16">A60</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">M</font>, <font color="Maroon" title="c3">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c4">o</font>, <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">a1</font>, <font color="Maroon" title="c9">b1</font>, <font color="Maroon" title="c10">c1</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="E1:22_2_1"/><i><font color="Green" title="E17">A61</font></i>: 
( <font color="Maroon" title="c2">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c3">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a1</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b1</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">c1</font> &amp; <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c8">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c9">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c10">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c9">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">a1</font> &amp; <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c10">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c9">b1</font> )
 ;<br/><a NAME="E2:22_2_1"/><i><font color="Green" title="E18">A62</font></i>: 
( not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; not <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; not <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; not <font color="Maroon" title="c8">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; not <font color="Maroon" title="c9">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; not <font color="Maroon" title="c10">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_2_1_1"/><i><font color="Green" title="E19">A63</font></i>: 
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c8">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> or <font color="Maroon" title="c9">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> or <font color="Maroon" title="c10">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> )
 ;<br/>

<a NAME="E2:22_2_1_1"/>
( <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c5">a</font> &amp; <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c8">a1</font> &amp; <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c9">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c9">b1</font> &amp; <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c10">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">o</font>,<font color="Maroon" title="c10">c1</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/>
<a NAME="E3:22_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:22_2_1"><i><font color="Green" title="E17">A61</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_2_1_1"><i><font color="Green" title="E19">A63</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<b>hence </b><a NAME="E4:22_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_2_1"><i><font color="Green" title="E17">A61</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:22_2_1"/><i><font color="Green" title="E19">A64</font></i>: 
( <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c9">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a1</font>,<font color="Maroon" title="c6">b</font> &amp; <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c10">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c7">c</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_2_1"><i><font color="Green" title="E17">A61</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E4:22_2_1"/>
<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c9">b1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><a NAME="E5:22_2_1"/><b>then </b>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c10">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">a1</font>,<font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22_2"><i><font color="Green" title="E16">A60</font></i></a>, <a class="txt" href="conmetr1.html#E1:22_2_1"><i><font color="Green" title="E17">A61</font></i></a>, <a class="txt" href="conmetr1.html#E2:22_2_1"><i><font color="Green" title="E18">A62</font></i></a>, <a class="txt" href="conmetr1.html#E3:22_2_1"><i><font color="Green" title="E19">A64</font></i></a>, <a class="ref" href="conmetr1.html#D6" target="_self" title="CONMETR1:def.6">Def6</a></i>;<br/><b>hence </b><a NAME="E6:22_2_1"/>
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c10">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:22_2"/>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a> 
 <b>by </b><i><a class="ref" href="aff_2.html#D2" title="AFF_2:def.2">AFF_2:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:22"/>
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR2" title="AFF_2:NR.2">satisfies_PAP</a>  iff <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR6" title="CONMETR1:NR.6">satisfies_major_SCH*</a>  )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:22"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>


</div>
