<?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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a>  iff <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a>  )</span><br/>

<a NAME="E1:20"/><i><font color="Green" title="E13">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a>  implies <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">Z</font>, <font color="Maroon" title="c4">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">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 <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b5">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b7">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c4">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">c1</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font></span><br/><b>let </b><font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">c1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c4">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font> implies <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> )</span><br/><b>assume </b><a NAME="E1:20_1_1"/><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c4">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font></span><br/><b>assume </b><a NAME="E2:20_1_1"/><i><font color="Green" title="E16">A4</font></i>: 
not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div><i><font color="Green" title="E17">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">Y</font>, <font color="Maroon" title="c13">Z</font>, <font color="Maroon" title="c14">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">c1</font>, <font color="Olive" title="b8">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Olive" title="b5">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Olive" title="b7">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c14">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b8">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font>,<font color="Olive" title="b8">d</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">a1</font>,<font color="Olive" title="b8">d</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font></span><br/><b>let </b><font color="Maroon" title="c15">o</font>, <font color="Maroon" title="c16">a</font>, <font color="Maroon" title="c17">b</font>, <font color="Maroon" title="c18">c</font>, <font color="Maroon" title="c19">a1</font>, <font color="Maroon" title="c20">b1</font>, <font color="Maroon" title="c21">c1</font>, <font color="Maroon" title="c22">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a>  &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c14">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c22">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c22">d</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> implies <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )</span><br/><b>assume </b><a NAME="E1:20_1_1_1"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c14">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c22">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c22">d</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> implies <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )</span><br/><b>assume </b><a NAME="E2:20_1_1_1"/><i><font color="Green" title="E19">A7</font></i>: 
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c14">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c22">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c22">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> or <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )</span><br/><a NAME="E3:20_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> or <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1"/><i><font color="Green" title="E20">A8</font></i>: 
( not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> &amp; not <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1"/><i><font color="Green" title="E21">A9</font></i>: 
( <font color="Maroon" title="c18">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1"/><i><font color="Green" title="E22">A10</font></i>: 
(  not <font color="Maroon" title="c18">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> or  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font> or  not <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E23">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_1_1"/><i><font color="Green" title="E24">A12</font></i>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_1_1"/><i><font color="Green" title="E25">A13</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E26">A14</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1_1_1"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_1_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E4:20_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E26">A15</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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/><a NAME="E6:20_1_1_1_1_1_1"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1_1"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E7:20_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E27">A16</font></i>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_1_1"><i><font color="Green" title="E25">A13</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_1_1"><i><font color="Green" title="E26">A15</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E8:20_1_1_1_1_1_1"/><i><font color="Green" title="E28">A17</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E29">A18</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1_1_2"><i><font color="Green" title="E29">A18</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_1_1_1_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E10:20_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E11:20_1_1_1_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</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="E12:20_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_1_1"><i><font color="Green" title="E27">A16</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_1_1"><i><font color="Green" title="E28">A17</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E13:20_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1_1"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E24">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_1_2"/><i><font color="Green" title="E25">A20</font></i>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_1_2"/><i><font color="Green" title="E26">A21</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_2_1"/><b>then </b><i><font color="Green" title="E27">A22</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1_2_1"><i><font color="Green" title="E27">A22</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_1_2"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E4:20_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_1_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</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="E6:20_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E27">A23</font></i>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1_2"><i><font color="Green" title="E25">A20</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_1_2"><i><font color="Green" title="E26">A21</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E7:20_1_1_1_1_1_2"/><i><font color="Green" title="E28">A24</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E29">A25</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_2_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1_2_2"><i><font color="Green" title="E29">A25</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E8:20_1_1_1_1_1_2"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E9:20_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E10:20_1_1_1_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">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="E11:20_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1_2"><i><font color="Green" title="E25">A20</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_1_2"><i><font color="Green" title="E28">A24</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E12:20_1_1_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_1_2"><i><font color="Green" title="E27">A23</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_1_3"/><i><font color="Green" title="E25">A26</font></i>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_1_3"/><i><font color="Green" title="E26">A27</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_3_1"/><b>then </b><i><font color="Green" title="E27">A28</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_3_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1_3_1"><i><font color="Green" title="E27">A28</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_1_3"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E4:20_1_1_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_1_1_1_3"/><b>then </b><i><font color="Green" title="E27">A29</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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/><a NAME="E6:20_1_1_1_1_1_3"/>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1_3"><i><font color="Green" title="E25">A26</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E7:20_1_1_1_1_1_3"/><b>then </b><i><font color="Green" title="E28">A30</font></i>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_1_3"><i><font color="Green" title="E26">A27</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_1_3"><i><font color="Green" title="E27">A29</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E8:20_1_1_1_1_1_3"/><i><font color="Green" title="E29">A31</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_3_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_1_3_2"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_3_2"/><b>then </b><i><font color="Green" title="E30">A32</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_3_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_3_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1_3_2"><i><font color="Green" title="E30">A32</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_1_1_1_3"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E10:20_1_1_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E11:20_1_1_1_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">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="E12:20_1_1_1_1_1_3"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_1_3"><i><font color="Green" title="E28">A30</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_1_3"><i><font color="Green" title="E29">A31</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E13:20_1_1_1_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1_3"><i><font color="Green" title="E25">A26</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_1"><i><font color="Green" title="E22">A10</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_1"><i><font color="Green" title="E23">A11</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_1"><i><font color="Green" title="E24">A19</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2"/><i><font color="Green" title="E22">A33</font></i>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><div><i><font color="Green" title="E23">A34</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_1"/><i><font color="Green" title="E24">A35</font></i>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_1"/><i><font color="Green" title="E25">A36</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_1"/><i><font color="Green" title="E26">A37</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_1_1"/><i><font color="Green" title="E27">A38</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E28">A39</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_1_1_1"><i><font color="Green" title="E28">A39</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_1_1"/><i><font color="Green" title="E28">A40</font></i>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1"><i><font color="Green" title="E24">A35</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1_1"><i><font color="Green" title="E26">A37</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c19">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/>
<a NAME="E4:20_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E29">A41</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E30">A42</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_1_2_1"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1"><i><font color="Green" title="E24">A35</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="E3:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_1_2_1"/><b>then </b><i><font color="Green" title="E31">A43</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_1_1_2_1"><i><font color="Green" title="E31">A43</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E7:20_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_1_1_2"><i><font color="Green" title="E29">A41</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_1_1_2"><i><font color="Green" title="E30">A42</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_1_1_2_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1_1"><i><font color="Green" title="E26">A37</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_1_1"><i><font color="Green" title="E27">A38</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_1_1"><i><font color="Green" title="E28">A40</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_1"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_2"/><i><font color="Green" title="E26">A44</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_1_2"/><i><font color="Green" title="E27">A45</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_2_1"/><b>then </b><i><font color="Green" title="E28">A46</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_1_2_1"><i><font color="Green" title="E28">A46</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_1_2"/><i><font color="Green" title="E28">A47</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_1_2_2"/><i><font color="Green" title="E29">A48</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_1"><i><font color="Green" title="E25">A36</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1_2"><i><font color="Green" title="E26">A44</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</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="E4:20_1_1_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</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="E7:20_1_1_1_1_2_1_2_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1_2_2"><i><font color="Green" title="E29">A48</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c21">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/>
<b>hence </b><a NAME="E9:20_1_1_1_1_2_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_1_1_2_1_2"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1_2"><i><font color="Green" title="E26">A44</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_1_2"><i><font color="Green" title="E27">A45</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_1_2"><i><font color="Green" title="E28">A47</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_1_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_1"><i><font color="Green" title="E24">A35</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2"/><i><font color="Green" title="E24">A49</font></i>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2"/><i><font color="Green" title="E25">A50</font></i>: 
( <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_1"/><i><font color="Green" title="E26">A51</font></i>: 
(  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> or  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E27">A52</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_1_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_1_1"/><b>then </b><i><font color="Green" title="E28">A53</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_1_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_1_1"><i><font color="Green" title="E28">A53</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_1_2"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E28">A54</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_1_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_1_2"><i><font color="Green" title="E28">A54</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_1_1_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_1"><i><font color="Green" title="E26">A51</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_1"><i><font color="Green" title="E27">A52</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_2"/><i><font color="Green" title="E26">A55</font></i>: 
( <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2"/><i><font color="Green" title="E27">A56</font></i>: 
(  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> or  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E28">A57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_1"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_2_1"/><b>then </b><i><font color="Green" title="E29">A58</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_2_1"><i><font color="Green" title="E29">A58</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_2"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_2_2"/><b>then </b><i><font color="Green" title="E29">A59</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_2_2"/><i><font color="Green" title="E30">A60</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_2_1"/><i><font color="Green" title="E31">A61</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_2_2_1"/><i><font color="Green" title="E32">A62</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b><i><font color="Green" title="E33">A63</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_2_2_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_2_2_1_1"><i><font color="Green" title="E33">A63</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_2_2_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_2_2_1"/><b>then </b><i><font color="Green" title="E33">A64</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_2_2_1"><i><font color="Green" title="E31">A61</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_2_2_1"><i><font color="Green" title="E33">A64</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c20">b1</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="E12:20_1_1_1_1_2_2_2_2_1"/><b>then </b><i><font color="Green" title="E34">A65</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</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="E13:20_1_1_1_1_2_2_2_2_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E15:20_1_1_1_1_2_2_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_2_2_1"><i><font color="Green" title="E32">A62</font></i></a>, <a class="txt" href="conmetr1.html#E12:20_1_1_1_1_2_2_2_2_1"><i><font color="Green" title="E34">A65</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_1_1_2_2_2_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_2_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_2_2"><i><font color="Green" title="E29">A59</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_2_2"><i><font color="Green" title="E30">A60</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_1_1_2_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_1_1_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_2"><i><font color="Green" title="E27">A56</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_2"><i><font color="Green" title="E28">A57</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_1_1_2_2"/><i><font color="Green" title="E27">A66</font></i>: 
( <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon" title="c23">A</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="E7:20_1_1_1_1_2_2"/><i><font color="Green" title="E28">A67</font></i>: 
( <font color="Maroon" title="c23">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</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="E8:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</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="c24">K</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="E10:20_1_1_1_1_2_2"/><i><font color="Green" title="E29">A68</font></i>: 
( <font color="Maroon" title="c24">K</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</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="E11:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</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="c25">C</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="E13:20_1_1_1_1_2_2"/><i><font color="Green" title="E30">A69</font></i>: 
( <font color="Maroon" title="c25">C</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</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="E14:20_1_1_1_1_2_2"/>
 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/>( <font color="Olive" title="b1">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Olive" title="b1">d1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_3"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c26">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="E2:20_1_1_1_1_2_2_3"/><i><font color="Green" title="E31">A70</font></i>: 
( <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c26">e1</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">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="c27">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="E4:20_1_1_1_1_2_2_3"/><i><font color="Green" title="E32">A71</font></i>: 
( <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">e2</font> &amp; <font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_3"/>
not <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c26">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_3_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c26">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_3"><i><font color="Green" title="E31">A70</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_3_1"/><b>then </b><i><font color="Green" title="E33">A72</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_3"><i><font color="Green" title="E32">A71</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_3_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_3_1"><i><font color="Green" title="E33">A72</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_3_1"/><b>then </b><i><font color="Green" title="E34">A73</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_3_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_3_1"><i><font color="Green" title="E34">A73</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E12:20_1_1_1_1_2_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c28">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="E7:20_1_1_1_1_2_2_3"/><i><font color="Green" title="E33">A74</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c26">e1</font>,<font color="Maroon" title="c28">d1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">e2</font>,<font color="Maroon" title="c28">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="c28">d1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c28">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d1</font> )</span><br/>

<a NAME="E8:20_1_1_1_1_2_2_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c26">e1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_3"><i><font color="Green" title="E31">A70</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="E9:20_1_1_1_1_2_2_3"/><b>then </b><i><font color="Green" title="E34">A75</font></i>: 
<font color="Maroon" title="c26">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_3"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_3"><i><font color="Green" title="E33">A74</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="E11:20_1_1_1_1_2_2_3"/>
( <font color="Maroon" title="c28">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d1</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_3"><i><font color="Green" title="E31">A70</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_3"><i><font color="Green" title="E32">A71</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_3"><i><font color="Green" title="E33">A74</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_3"><i><font color="Green" title="E34">A75</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c26">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="E16:20_1_1_1_1_2_2"/><i><font color="Green" title="E31">A76</font></i>: 
( <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> )
 ;<br/><a NAME="E17:20_1_1_1_1_2_2"/>
 ex <font color="Olive" title="b1">d2</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">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Olive" title="b1">d2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_4"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c27">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="E2:20_1_1_1_1_2_2_4"/><i><font color="Green" title="E32">A77</font></i>: 
( <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c27">e1</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">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="c28">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="E4:20_1_1_1_1_2_2_4"/><i><font color="Green" title="E33">A78</font></i>: 
( <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">e2</font> &amp; <font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_4"/>
not <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c27">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_4_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c27">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_4"><i><font color="Green" title="E32">A77</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_4"><i><font color="Green" title="E33">A78</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</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="E6:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_4_1"/><b>then </b><i><font color="Green" title="E34">A79</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_4_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_4_1"><i><font color="Green" title="E34">A79</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_1_1_2_2_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c29">d2</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="E7:20_1_1_1_1_2_2_4"/><i><font color="Green" title="E34">A80</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c27">e1</font>,<font color="Maroon" title="c29">d2</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">e2</font>,<font color="Maroon" title="c29">d2</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="c29">d2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c29">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c29">d2</font> )</span><br/>

<a NAME="E8:20_1_1_1_1_2_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c27">e1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_4"><i><font color="Green" title="E32">A77</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="E9:20_1_1_1_1_2_2_4"/><b>then </b><i><font color="Green" title="E35">A81</font></i>: 
<font color="Maroon" title="c27">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_4"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c29">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_4"><i><font color="Green" title="E34">A80</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="E11:20_1_1_1_1_2_2_4"/>
( <font color="Maroon" title="c29">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c29">d2</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_4"><i><font color="Green" title="E32">A77</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_4"><i><font color="Green" title="E33">A78</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_4"><i><font color="Green" title="E34">A80</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_4"><i><font color="Green" title="E35">A81</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c27">d2</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="E19:20_1_1_1_1_2_2"/><i><font color="Green" title="E32">A82</font></i>: 
( <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">d2</font> )
 ;<br/><a NAME="E20:20_1_1_1_1_2_2"/>
 ex <font color="Olive" title="b1">d3</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">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Olive" title="b1">d3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_5"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c28">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="E2:20_1_1_1_1_2_2_5"/><i><font color="Green" title="E33">A83</font></i>: 
( <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">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="c29">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="E4:20_1_1_1_1_2_2_5"/><i><font color="Green" title="E34">A84</font></i>: 
( <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">e2</font> &amp; <font color="Maroon" title="c26">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_5"/>
not <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_5_1"/>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_5"><i><font color="Green" title="E33">A83</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_5_1"/><b>then </b><i><font color="Green" title="E35">A85</font></i>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_5"><i><font color="Green" title="E34">A84</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_5_1"/><b>then </b><i><font color="Green" title="E36">A86</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_5_1"/><i><font color="Green" title="E37">A87</font></i>: 
( <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_5_1"/><b>then </b><i><font color="Green" title="E38">A88</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_5_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_2_2_5_1"><i><font color="Green" title="E37">A87</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_5_1"><i><font color="Green" title="E36">A86</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_5_1"><i><font color="Green" title="E38">A88</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E14:20_1_1_1_1_2_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</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="E15:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">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="E17:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_5_1"><i><font color="Green" title="E38">A88</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="E18:20_1_1_1_1_2_2_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_5_1"><i><font color="Green" title="E35">A85</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c30">d3</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="E7:20_1_1_1_1_2_2_5"/><i><font color="Green" title="E35">A89</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font>,<font color="Maroon" title="c30">d3</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">e2</font>,<font color="Maroon" title="c30">d3</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="c30">d3</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c30">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">d3</font> )</span><br/>

<a NAME="E8:20_1_1_1_1_2_2_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c28">e1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_5"><i><font color="Green" title="E33">A83</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="E9:20_1_1_1_1_2_2_5"/><b>then </b><i><font color="Green" title="E36">A90</font></i>: 
<font color="Maroon" title="c28">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_5"/>
<font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">d3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_5"><i><font color="Green" title="E35">A89</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="E11:20_1_1_1_1_2_2_5"/>
( <font color="Maroon" title="c30">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">d3</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_5"><i><font color="Green" title="E33">A83</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_5"><i><font color="Green" title="E34">A84</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_5"><i><font color="Green" title="E35">A89</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_5"><i><font color="Green" title="E36">A90</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c28">d3</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="E22:20_1_1_1_1_2_2"/><i><font color="Green" title="E33">A91</font></i>: 
( <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> )
 ;<br/><a NAME="E23:20_1_1_1_1_2_2"/>
 ex <font color="Olive" title="b1">d4</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">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Olive" title="b1">d4</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c29">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="E2:20_1_1_1_1_2_2_6"/><i><font color="Green" title="E34">A92</font></i>: 
( <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c29">e1</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">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="c30">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="E4:20_1_1_1_1_2_2_6"/><i><font color="Green" title="E35">A93</font></i>: 
( <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">e2</font> &amp; <font color="Maroon" title="c26">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6"/>
not <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c29">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1"/>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c29">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_6"><i><font color="Green" title="E34">A92</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green" title="E36">A94</font></i>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_6"><i><font color="Green" title="E35">A93</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1"/><i><font color="Green" title="E37">A95</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green" title="E38">A96</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green" title="E39">A97</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_1_1"/><i><font color="Green" title="E40">A98</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_1_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b><i><font color="Green" title="E41">A99</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_1_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_6_1_1_1"><i><font color="Green" title="E40">A98</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_6_1_1_1"><i><font color="Green" title="E41">A99</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_6_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green" title="E40">A100</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green" title="E41">A101</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E38">A96</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E39">A97</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E40">A100</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6_1_1"/>
<font color="Maroon" title="c23">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green" title="E42">A102</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E41">A101</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</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="E12:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</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="E13:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green" title="E43">A103</font></i>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green" title="E44">A104</font></i>: 
( <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green" title="E45">A105</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_6_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E15:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E44">A104</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E42">A102</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E19:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E45">A105</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E20:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E21:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</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="E22:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">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="E24:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E45">A105</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="E25:20_1_1_1_1_2_2_6_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_1_1_2_2_6_1_1"><i><font color="Green" title="E43">A103</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:20_1_1_1_1_2_2_6_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green" title="E38">A106</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green" title="E39">A107</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E36">A94</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E37">A95</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E10:20_1_1_1_1_2_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">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="E11:20_1_1_1_1_2_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</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="E12:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">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="E13:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green" title="E40">A108</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E38">A106</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_6_1"/><i><font color="Green" title="E41">A109</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_2"/><i><font color="Green" title="E42">A110</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_2"/><i><font color="Green" title="E43">A111</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b><i><font color="Green" title="E44">A112</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_6_1_2_1"><i><font color="Green" title="E44">A112</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_6_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_6_1_2"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_2"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_2"/><b>then </b><i><font color="Green" title="E44">A113</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">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/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_2"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_6_1_2_2"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2"><i><font color="Green" title="E26">A55</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_6_1_2"><i><font color="Green" title="E42">A110</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">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/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b><i><font color="Green" title="E45">A114</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1_2_2"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_6_1_2_2"><i><font color="Green" title="E45">A114</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">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="E12:20_1_1_1_1_2_2_6_1_2_2"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_6_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2"><i><font color="Green" title="E26">A55</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_6_1_2"><i><font color="Green" title="E42">A110</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_6_1_2"><i><font color="Green" title="E43">A111</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_6_1_2"><i><font color="Green" title="E44">A113</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E15:20_1_1_1_1_2_2_6_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E40">A108</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E41">A109</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</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="E19:20_1_1_1_1_2_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E20:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</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="E21:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E22:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E38">A106</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="E23:20_1_1_1_1_2_2_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_2_2_6_1"><i><font color="Green" title="E39">A107</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c31">d4</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="E7:20_1_1_1_1_2_2_6"/><i><font color="Green" title="E36">A115</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c29">e1</font>,<font color="Maroon" title="c31">d4</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">e2</font>,<font color="Maroon" title="c31">d4</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="c31">d4</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c31">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c31">d4</font> )</span><br/>

<a NAME="E8:20_1_1_1_1_2_2_6"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c29">e1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_6"><i><font color="Green" title="E34">A92</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="E9:20_1_1_1_1_2_2_6"/><b>then </b><i><font color="Green" title="E37">A116</font></i>: 
<font color="Maroon" title="c29">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6"/>
<font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c30">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c31">d4</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_6"><i><font color="Green" title="E36">A115</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="E11:20_1_1_1_1_2_2_6"/>
( <font color="Maroon" title="c31">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c31">d4</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_6"><i><font color="Green" title="E34">A92</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_6"><i><font color="Green" title="E35">A93</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_6"><i><font color="Green" title="E36">A115</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_6"><i><font color="Green" title="E37">A116</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c29">d4</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="E25:20_1_1_1_1_2_2"/><i><font color="Green" title="E34">A117</font></i>: 
( <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">d4</font> )
 ;<br/><a NAME="E26:20_1_1_1_1_2_2"/><i><font color="Green" title="E35">A118</font></i>: 
( <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2"><i><font color="Green" title="E22">A33</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E27:20_1_1_1_1_2_2"/><i><font color="Green" title="E36">A119</font></i>: 
( not <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; not <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; not <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7"/><i><font color="Green" title="E37">A120</font></i>: 
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> or <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> or <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> or <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E38">A121</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_1"/><i><font color="Green" title="E39">A122</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_7_1"/>
<font color="Maroon" title="c23">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_7_1"/><b>then </b><i><font color="Green" title="E40">A123</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7_1"><i><font color="Green" title="E39">A122</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</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="E5:20_1_1_1_1_2_2_7_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</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="E6:20_1_1_1_1_2_2_7_1"/><b>then </b><i><font color="Green" title="E41">A124</font></i>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_7_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_7_1"/><b>then </b><i><font color="Green" title="E42">A125</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_7_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E10:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E11:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7_1"><i><font color="Green" title="E40">A123</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_2_2_7_1"><i><font color="Green" title="E42">A125</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E13:20_1_1_1_1_2_2_7_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E14:20_1_1_1_1_2_2_7_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</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="E15:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E16:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">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="E17:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_2_2_7_1"><i><font color="Green" title="E42">A125</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E18:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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/><b>hence </b><a NAME="E19:20_1_1_1_1_2_2_7_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_7_1"><i><font color="Green" title="E41">A124</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E39">A126</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2"/><i><font color="Green" title="E40">A127</font></i>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_7_2"/>
<font color="Maroon" title="c23">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_7_2"/><b>then </b><i><font color="Green" title="E41">A128</font></i>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E40">A127</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_2"/><i><font color="Green" title="E42">A129</font></i>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_7_2_1"/><b>then </b><i><font color="Green" title="E43">A130</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_2_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7_2_1"><i><font color="Green" title="E43">A130</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:20_1_1_1_1_2_2_7_2"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2_2"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_7_2_2"/><b>then </b><i><font color="Green" title="E43">A131</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_2_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_2_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7_2_2"><i><font color="Green" title="E43">A131</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E6:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E41">A128</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E42">A129</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E9:20_1_1_1_1_2_2_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c19">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/><a NAME="E10:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c19">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/><a NAME="E11:20_1_1_1_1_2_2_7_2"/><b>then </b><i><font color="Green" title="E43">A132</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E12:20_1_1_1_1_2_2_7_2"/><i><font color="Green" title="E44">A133</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2_3"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_7_2_3"/><b>then </b><i><font color="Green" title="E45">A134</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_2_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_2_3"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7_2_3"><i><font color="Green" title="E45">A134</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:20_1_1_1_1_2_2_7_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E41">A128</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="E14:20_1_1_1_1_2_2_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E15:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E16:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E17:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E42">A129</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="E18:20_1_1_1_1_2_2_7_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E43">A132</font></i></a>, <a class="txt" href="conmetr1.html#E12:20_1_1_1_1_2_2_7_2"><i><font color="Green" title="E44">A133</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E40">A135</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_3"/><i><font color="Green" title="E41">A136</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_7_3"/><i><font color="Green" title="E42">A137</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_3_1"/><i><font color="Green" title="E43">A138</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_7_3_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_3_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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/>
<a NAME="E5:20_1_1_1_1_2_2_7_3_1"/><b>then </b><i><font color="Green" title="E44">A139</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_7_3_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_7_3_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7_3_1"><i><font color="Green" title="E43">A138</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_7_3_1"><i><font color="Green" title="E44">A139</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_7_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_2_7_3"/><i><font color="Green" title="E43">A140</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_3"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_7_3"/><b>then </b><i><font color="Green" title="E44">A141</font></i>: 
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7_3"><i><font color="Green" title="E41">A136</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7_3"><i><font color="Green" title="E42">A137</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7_3"><i><font color="Green" title="E43">A140</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_7_3"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_7_3"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_7_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_7_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7"><i><font color="Green" title="E38">A121</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_7_3"><i><font color="Green" title="E44">A141</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_4"/><i><font color="Green" title="E41">A142</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_7_4"/><i><font color="Green" title="E42">A143</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_4_1"/><i><font color="Green" title="E43">A144</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_7_4_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_4_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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/>
<a NAME="E5:20_1_1_1_1_2_2_7_4_1"/><b>then </b><i><font color="Green" title="E44">A145</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_7_4_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_7_4_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7_4_1"><i><font color="Green" title="E43">A144</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_7_4_1"><i><font color="Green" title="E44">A145</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_7_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_2_7_4"/><i><font color="Green" title="E43">A146</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_4"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7"><i><font color="Green" title="E39">A126</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7_4"><i><font color="Green" title="E41">A142</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7_4"><i><font color="Green" title="E42">A143</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7_4"><i><font color="Green" title="E43">A146</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_7"><i><font color="Green" title="E37">A120</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_7"><i><font color="Green" title="E38">A121</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_7"><i><font color="Green" title="E39">A126</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_7"><i><font color="Green" title="E40">A135</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E28:20_1_1_1_1_2_2"/><i><font color="Green" title="E37">A147</font></i>: 
( not <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; not <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; not <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; not <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8"/><i><font color="Green" title="E38">A148</font></i>: 
( <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> or <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> or <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> or <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E39">A149</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_1"/><i><font color="Green" title="E40">A150</font></i>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_8_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_8_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8_1"><i><font color="Green" title="E40">A150</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_8_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</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="E5:20_1_1_1_1_2_2_8_1"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_8_1"/><b>then </b><i><font color="Green" title="E41">A151</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_8_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_8_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_8_1"><i><font color="Green" title="E41">A151</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_8_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E40">A152</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_2"/><i><font color="Green" title="E41">A153</font></i>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_8_2"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_8_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8_2"><i><font color="Green" title="E41">A153</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_8_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_8_2"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_8_2"/><b>then </b><i><font color="Green" title="E42">A154</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_8_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_8_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_8_2"><i><font color="Green" title="E42">A154</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_8_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E41">A155</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_3"/><i><font color="Green" title="E42">A156</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_8_3"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_8_3"/><b>then </b><i><font color="Green" title="E43">A157</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8_3"><i><font color="Green" title="E42">A156</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_8_3"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_8_3"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_8_3"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_8_3"><i><font color="Green" title="E43">A157</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="E7:20_1_1_1_1_2_2_8_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_4"/><i><font color="Green" title="E42">A158</font></i>: 
<font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_8_4"/><i><font color="Green" title="E43">A159</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_4_1"/><i><font color="Green" title="E44">A160</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_8_4_1"/><i><font color="Green" title="E45">A161</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_4_1_1"/><i><font color="Green" title="E46">A162</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_8_4_1_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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/>
<a NAME="E5:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b><i><font color="Green" title="E47">A163</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_8_4_1_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8_4_1_1"><i><font color="Green" title="E46">A162</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_8_4_1_1"><i><font color="Green" title="E47">A163</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_8_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_8_4_1"/><i><font color="Green" title="E46">A164</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_8_4_1"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green" title="E47">A165</font></i>: 
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E44">A160</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E45">A161</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E46">A164</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_8_4_1"/>
<font color="Maroon" title="c23">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c23">A</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green" title="E48">A166</font></i>: 
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E47">A165</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_8_4_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E48">A166</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green" title="E49">A167</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green" title="E50">A168</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</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="E14:20_1_1_1_1_2_2_8_4_1"/>
( <font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green" title="E51">A169</font></i>: 
( <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E50">A168</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E15:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E51">A169</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E19:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</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="E20:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">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="E22:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green" title="E52">A170</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E15:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E51">A169</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E23:20_1_1_1_1_2_2_8_4_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E11:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E49">A167</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E24:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E25:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E26:20_1_1_1_1_2_2_8_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2_8_4_1"><i><font color="Green" title="E52">A170</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_2_8_4"/>
<font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_1_1_2_2_8_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_8"><i><font color="Green" title="E40">A152</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8_4"><i><font color="Green" title="E42">A158</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_8_4"><i><font color="Green" title="E43">A159</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_8"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_8"><i><font color="Green" title="E38">A148</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_8"><i><font color="Green" title="E39">A149</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_8"><i><font color="Green" title="E40">A152</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_8"><i><font color="Green" title="E41">A155</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E29:20_1_1_1_1_2_2"/><i><font color="Green" title="E38">A171</font></i>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c22">d</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E30:20_1_1_1_1_2_2"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_9"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_9"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_9"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_9"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E31:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E39">A172</font></i>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c28">d3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="txt" href="conmetr1.html#E26:20_1_1_1_1_2_2"><i><font color="Green" title="E35">A118</font></i></a>, <a class="txt" href="conmetr1.html#E27:20_1_1_1_1_2_2"><i><font color="Green" title="E36">A119</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="txt" href="conmetr1.html#E29:20_1_1_1_1_2_2"><i><font color="Green" title="E38">A171</font></i></a>, <a class="ref" href="conmetr1.html#D3" target="_self" title="CONMETR1:def.3">Def3</a></i>;<br/><a NAME="E32:20_1_1_1_1_2_2"/><i><font color="Green" title="E40">A173</font></i>: 
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_10"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_10_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_10_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_10_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">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="E4:20_1_1_1_1_2_2_10_1"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_1_1_1_1_2_2_10"/>
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E33:20_1_1_1_1_2_2"/><i><font color="Green" title="E41">A174</font></i>: 
( <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_11"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_11"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_11_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_11_1"/>
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>;<br/>
<b>hence </b><a NAME="E2:20_1_1_1_1_2_2_11_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_1_1_1_1_2_2_11"/>
( <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E25:20_1_1_1_1_2_2"><i><font color="Green" title="E34">A117</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E34:20_1_1_1_1_2_2"/><i><font color="Green" title="E42">A175</font></i>: 
( not <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; not <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12"/><i><font color="Green" title="E43">A176</font></i>: 
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> or <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> or <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> or <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E44">A177</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1"/><i><font color="Green" title="E45">A178</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_12_1"/>
<font color="Maroon" title="c24">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c24">K</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green" title="E46">A179</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_1"><i><font color="Green" title="E45">A178</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E5:20_1_1_1_1_2_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</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="E6:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green" title="E47">A180</font></i>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_12_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green" title="E48">A181</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green" title="E49">A182</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_1"><i><font color="Green" title="E46">A179</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E10:20_1_1_1_1_2_2_12_1"/><i><font color="Green" title="E50">A183</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green" title="E51">A184</font></i>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green" title="E52">A185</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1_1"/><i><font color="Green" title="E53">A186</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1_1"/><i><font color="Green" title="E54">A187</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b><i><font color="Green" title="E55">A188</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_12_1_1_1_1"><i><font color="Green" title="E55">A188</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b><i><font color="Green" title="E55">A189</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_1_1_1"><i><font color="Green" title="E53">A186</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_12_1_1_1"><i><font color="Green" title="E55">A189</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c20">b1</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="E12:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b><i><font color="Green" title="E56">A190</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</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="E13:20_1_1_1_1_2_2_12_1_1_1"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E15:20_1_1_1_1_2_2_12_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12_1_1_1"><i><font color="Green" title="E54">A187</font></i></a>, <a class="txt" href="conmetr1.html#E12:20_1_1_1_1_2_2_12_1_1_1"><i><font color="Green" title="E56">A190</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green" title="E53">A191</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b><i><font color="Green" title="E54">A192</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_12_1_1_2"><i><font color="Green" title="E54">A192</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green" title="E54">A193</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_12_1_1_3"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b><i><font color="Green" title="E55">A194</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_1_1"><i><font color="Green" title="E51">A184</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12_1_1"><i><font color="Green" title="E52">A185</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12_1_1_3"><i><font color="Green" title="E55">A194</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">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="E10:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">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="E11:20_1_1_1_1_2_2_12_1_1_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12_1_1"><i><font color="Green" title="E52">A185</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_1_1"><i><font color="Green" title="E53">A191</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_12_1_1"><i><font color="Green" title="E54">A193</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E11:20_1_1_1_1_2_2_12_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E13:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E9:20_1_1_1_1_2_2_12_1"><i><font color="Green" title="E49">A182</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2_12_1"><i><font color="Green" title="E50">A183</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E14:20_1_1_1_1_2_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</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="E15:20_1_1_1_1_2_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</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="E16:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E17:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E18:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_1_1_2_2_12_1"><i><font color="Green" title="E48">A181</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E19:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E20:20_1_1_1_1_2_2_12_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_12_1"><i><font color="Green" title="E47">A180</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E45">A195</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_2"/><i><font color="Green" title="E46">A196</font></i>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_12_2"/>
<font color="Maroon" title="c24">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c24">K</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_2"/><b>then </b><i><font color="Green" title="E47">A197</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_2"><i><font color="Green" title="E46">A196</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E5:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c19">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/><a NAME="E6:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c19">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/><a NAME="E7:20_1_1_1_1_2_2_12_2"/><b>then </b><i><font color="Green" title="E48">A198</font></i>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">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="E8:20_1_1_1_1_2_2_12_2"/>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2"><i><font color="Green" title="E26">A55</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_2"><i><font color="Green" title="E47">A197</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2"><i><font color="Green" title="E26">A55</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E10:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</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="E11:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E13:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E14:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2"><i><font color="Green" title="E25">A50</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="E15:20_1_1_1_1_2_2_12_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2"><i><font color="Green" title="E26">A55</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_12_2"><i><font color="Green" title="E48">A198</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E46">A199</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_3"/><i><font color="Green" title="E47">A200</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_12_3"/><i><font color="Green" title="E48">A201</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_3"/><i><font color="Green" title="E49">A202</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_3_1"/><i><font color="Green" title="E50">A203</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_12_3_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_3_1"/><b>then </b><i><font color="Green" title="E51">A204</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_3_1"><i><font color="Green" title="E50">A203</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_3_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_3_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_3_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_3_1"><i><font color="Green" title="E51">A204</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="E7:20_1_1_1_1_2_2_12_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_1_1_2_2_12_3"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_12_3"/><b>then </b><i><font color="Green" title="E50">A205</font></i>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_3"><i><font color="Green" title="E47">A200</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12_3"><i><font color="Green" title="E48">A201</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_3"><i><font color="Green" title="E49">A202</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_12_3"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_12_3"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_12_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_12_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12"><i><font color="Green" title="E44">A177</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_1_1_2_2_12_3"><i><font color="Green" title="E50">A205</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_4"/><i><font color="Green" title="E47">A206</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_12_4"/><i><font color="Green" title="E48">A207</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_4"/><i><font color="Green" title="E49">A208</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_4_1"/><i><font color="Green" title="E50">A209</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_12_4_1"/>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_4_1"/><b>then </b><i><font color="Green" title="E51">A210</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_4_1"/>
<font color="Maroon" title="c25">C</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c25">C</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_4_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_4_1"><i><font color="Green" title="E50">A209</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_4_1"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_4_1"><i><font color="Green" title="E51">A210</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="E7:20_1_1_1_1_2_2_12_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_1_1_2_2_12_4"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2"><i><font color="Green" title="E25">A50</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_12_4"/><b>then </b>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c19">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/><b>hence </b><a NAME="E6:20_1_1_1_1_2_2_12_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12"><i><font color="Green" title="E45">A195</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12_4"><i><font color="Green" title="E47">A206</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12_4"><i><font color="Green" title="E48">A207</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12_4"><i><font color="Green" title="E49">A208</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_12"><i><font color="Green" title="E43">A176</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_12"><i><font color="Green" title="E44">A177</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_12"><i><font color="Green" title="E45">A195</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_12"><i><font color="Green" title="E46">A199</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E35:20_1_1_1_1_2_2"/><i><font color="Green" title="E43">A211</font></i>: 
( not <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; not <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; not <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> &amp; not <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13"/><i><font color="Green" title="E44">A212</font></i>: 
( <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> or <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> or <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> or <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E45">A213</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13_1"/><i><font color="Green" title="E46">A214</font></i>: 
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_13_1"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_13_1"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c18">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_1_1_2_2_13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="txt" href="conmetr1.html#E34:20_1_1_1_1_2_2"><i><font color="Green" title="E42">A175</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_13_1"><i><font color="Green" title="E46">A214</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E46">A215</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13_2"/><i><font color="Green" title="E47">A216</font></i>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_13_2"/>
<font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_13_2"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_1_1_2_2_13_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_13_2"><i><font color="Green" title="E47">A216</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13_3"/><i><font color="Green" title="E47">A217</font></i>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_1_1_2_2_13_3"/>
<font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">d4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E25:20_1_1_1_1_2_2"><i><font color="Green" title="E34">A117</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E3:20_1_1_1_1_2_2_13_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E25:20_1_1_1_1_2_2"><i><font color="Green" title="E34">A117</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="txt" href="conmetr1.html#E34:20_1_1_1_1_2_2"><i><font color="Green" title="E42">A175</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_13_3"><i><font color="Green" title="E47">A217</font></i></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_13"><i><font color="Green" title="E44">A212</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_13"><i><font color="Green" title="E45">A213</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_13"><i><font color="Green" title="E46">A215</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E36:20_1_1_1_1_2_2"/><i><font color="Green" title="E44">A218</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c22">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_14"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_14_1"/><i><font color="Green" title="E45">A219</font></i>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_14_1"/><i><font color="Green" title="E46">A220</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_14_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_14_1"><i><font color="Green" title="E45">A219</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_14_1"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_14_1"><i><font color="Green" title="E46">A220</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:20_1_1_1_1_2_2_14"/><b>then </b>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c27">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</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="E3:20_1_1_1_1_2_2_14"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c22">d</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E37:20_1_1_1_1_2_2"/><i><font color="Green" title="E45">A221</font></i>: 
<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_15"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_15"/>
<font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_15"/><b>then </b>
<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_15"/>
<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E38:20_1_1_1_1_2_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_16"/><i><font color="Green" title="E46">A222</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T65" title="AFF_1:th.65">AFF_1:65</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_16"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">d4</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="txt" href="conmetr1.html#E25:20_1_1_1_1_2_2"><i><font color="Green" title="E34">A117</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</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="E3:20_1_1_1_1_2_2_16"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c29">d4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_16"><i><font color="Green" title="E46">A222</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E39:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E46">A223</font></i>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">d4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E32:20_1_1_1_1_2_2"><i><font color="Green" title="E40">A173</font></i></a>, <a class="txt" href="conmetr1.html#E33:20_1_1_1_1_2_2"><i><font color="Green" title="E41">A174</font></i></a>, <a class="txt" href="conmetr1.html#E34:20_1_1_1_1_2_2"><i><font color="Green" title="E42">A175</font></i></a>, <a class="txt" href="conmetr1.html#E35:20_1_1_1_1_2_2"><i><font color="Green" title="E43">A211</font></i></a>, <a class="txt" href="conmetr1.html#E36:20_1_1_1_1_2_2"><i><font color="Green" title="E44">A218</font></i></a>, <a class="txt" href="conmetr1.html#E37:20_1_1_1_1_2_2"><i><font color="Green" title="E45">A221</font></i></a>, <a class="ref" href="conmetr1.html#D3" target="_self" title="CONMETR1:def.3">Def3</a></i>;<br/><a NAME="E40:20_1_1_1_1_2_2"/><i><font color="Green" title="E47">A224</font></i>: 
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_17"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_17"/>
<font color="Maroon" title="c26">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</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="E4:20_1_1_1_1_2_2_17"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c16">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_17"/><b>then </b><i><font color="Green" title="E48">A225</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_17"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon" title="c12">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_1_1_2_2_17"><i><font color="Green" title="E48">A225</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E9:20_1_1_1_1_2_2_17"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E41:20_1_1_1_1_2_2"/><i><font color="Green" title="E48">A226</font></i>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_18"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_18"/><i><font color="Green" title="E49">A227</font></i>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_18"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_18_1"/><i><font color="Green" title="E50">A228</font></i>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_18_1"/><i><font color="Green" title="E51">A229</font></i>: 
( <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2"><i><font color="Green" title="E27">A66</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_18_1"/><i><font color="Green" title="E52">A230</font></i>: 
( <font color="Maroon" title="c23">A</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c23">A</font> &amp; <font color="Maroon" title="c24">K</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c24">K</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_18_1"/><b>then </b><i><font color="Green" title="E53">A231</font></i>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E10:20_1_1_1_1_2_2"><i><font color="Green" title="E29">A68</font></i></a>, <a class="txt" href="conmetr1.html#E25:20_1_1_1_1_2_2"><i><font color="Green" title="E34">A117</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_18"><i><font color="Green" title="E49">A227</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_18_1"><i><font color="Green" title="E51">A229</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_18_1"/>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d3</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2"><i><font color="Green" title="E28">A67</font></i></a>, <a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2_18_1"><i><font color="Green" title="E51">A229</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_18_1"><i><font color="Green" title="E52">A230</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_18_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2_18_1"><i><font color="Green" title="E50">A228</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_18_1"><i><font color="Green" title="E53">A231</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_18"/><b>then </b><i><font color="Green" title="E50">A232</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E22:20_1_1_1_1_2_2"><i><font color="Green" title="E33">A91</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_18"/><i><font color="Green" title="E51">A233</font></i>: 
( <font color="Maroon" title="c14">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c13">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">Z</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_18"/><b>then </b><i><font color="Green" title="E52">A234</font></i>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E28:20_1_1_1_1_2_2"><i><font color="Green" title="E37">A147</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2_18"><i><font color="Green" title="E50">A232</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_18"/><b>then </b><i><font color="Green" title="E53">A235</font></i>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_18"/><i><font color="Green" title="E54">A236</font></i>: 
( <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_1_1_2_2_18"><i><font color="Green" title="E51">A233</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_1_1_2_2_18"><i><font color="Green" title="E52">A234</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E12:20_1_1_1_1_2_2_18"><i><font color="Green" title="E54">A236</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">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="E16:20_1_1_1_1_2_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</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="E17:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">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="E19:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1_2_2"><i><font color="Green" title="E24">A49</font></i></a>, <a class="txt" href="conmetr1.html#E12:20_1_1_1_1_2_2_18"><i><font color="Green" title="E54">A236</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="E20:20_1_1_1_1_2_2_18"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_1_1_2_2_18"><i><font color="Green" title="E53">A235</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E42:20_1_1_1_1_2_2"/>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2_2"><i><font color="Green" title="E25">A50</font></i></a>, <a class="txt" href="conmetr1.html#E31:20_1_1_1_1_2_2"><i><font color="Green" title="E39">A172</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E43:20_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">d4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1_1_1_2_2"><i><font color="Green" title="E26">A55</font></i></a>, <a class="txt" href="conmetr1.html#E39:20_1_1_1_1_2_2"><i><font color="Green" title="E46">A223</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E44:20_1_1_1_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c29">d4</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="E45:20_1_1_1_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c27">d2</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="E46:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E49">A237</font></i>: 
<font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c27">d2</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="E47:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c29">d4</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E25:20_1_1_1_1_2_2"><i><font color="Green" title="E34">A117</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="E48:20_1_1_1_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c26">d1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E49:20_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c26">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="E50:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green" title="E50">A238</font></i>: 
<font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c26">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E41:20_1_1_1_1_2_2"><i><font color="Green" title="E48">A226</font></i></a>, <a class="txt" href="conmetr1.html#E46:20_1_1_1_1_2_2"><i><font color="Green" title="E49">A237</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E51:20_1_1_1_1_2_2"/>
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c26">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_19"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_19"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c26">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_1_1_2_2_19"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d1</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">d4</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="E3:20_1_1_1_1_2_2_19"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:20_1_1_1_1_2_2"><i><font color="Green" title="E30">A69</font></i></a>, <a class="txt" href="conmetr1.html#E16:20_1_1_1_1_2_2"><i><font color="Green" title="E31">A76</font></i></a>, <a class="txt" href="conmetr1.html#E19:20_1_1_1_1_2_2"><i><font color="Green" title="E32">A82</font></i></a>, <a class="txt" href="conmetr1.html#E35:20_1_1_1_1_2_2"><i><font color="Green" title="E43">A211</font></i></a>, <a class="txt" href="conmetr1.html#E40:20_1_1_1_1_2_2"><i><font color="Green" title="E47">A224</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E52:20_1_1_1_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E50:20_1_1_1_1_2_2"><i><font color="Green" title="E50">A238</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_1_1_2"><i><font color="Green" title="E23">A34</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> or <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E18">A239</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_2"/>
<font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_2"/><b>then </b><i><font color="Green" title="E19">A240</font></i>: 
( <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/><a NAME="E3:20_1_1_2"/>
<font color="Maroon" title="c4">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_2"><i><font color="Green" title="E19">A240</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3"/><i><font color="Green" title="E19">A241</font></i>: 
not <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3"/><i><font color="Green" title="E20">A242</font></i>: 
( <font color="Maroon" title="c2">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c4">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_3"/><i><font color="Green" title="E21">A243</font></i>: 
( not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_1"/><i><font color="Green" title="E22">A244</font></i>: 
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> or <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E23">A245</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_1_1"/><b>then </b><i><font color="Green" title="E24">A246</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_3_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_3_1_1"/><b>then </b>
<font color="Maroon" title="c2">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">Z</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_1_1"><i><font color="Green" title="E24">A246</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_1_2"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_1_2"/><b>then </b><i><font color="Green" title="E24">A247</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_3_1_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c2">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_1_2"><i><font color="Green" title="E24">A247</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_1"><i><font color="Green" title="E22">A244</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_1"><i><font color="Green" title="E23">A245</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_3"/><i><font color="Green" title="E22">A248</font></i>: 
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a1</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2"/><i><font color="Green" title="E23">A249</font></i>: 
(  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a1</font> or  not <font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> or  not <font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E24">A250</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_2_1"/><i><font color="Green" title="E25">A251</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_2_1"/><i><font color="Green" title="E26">A252</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_2_1"/><i><font color="Green" title="E27">A253</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_2_1"><i><font color="Green" title="E25">A251</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="E4:20_1_1_3_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_3_2_1"/><b>then </b><i><font color="Green" title="E28">A254</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_2_1"><i><font color="Green" title="E26">A252</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_2_1"><i><font color="Green" title="E27">A253</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E6:20_1_1_3_2_1"/><i><font color="Green" title="E29">A255</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E7:20_1_1_3_2_1"/><i><font color="Green" title="E30">A256</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_2_1"><i><font color="Green" title="E25">A251</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E8:20_1_1_3_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E9:20_1_1_3_2_1"/><b>then </b>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E6:20_1_1_3_2_1"><i><font color="Green" title="E29">A255</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_3_2_1"><i><font color="Green" title="E30">A256</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E10:20_1_1_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_2_1"><i><font color="Green" title="E28">A254</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E25">A257</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_2_2"/><i><font color="Green" title="E26">A258</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_2_2"/><i><font color="Green" title="E27">A259</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_3_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_2_2"><i><font color="Green" title="E26">A258</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E4:20_1_1_3_2_2"/><b>then </b><i><font color="Green" title="E28">A260</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">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/><a NAME="E5:20_1_1_3_2_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_3_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_2"><i><font color="Green" title="E24">A250</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_2_2"><i><font color="Green" title="E27">A259</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_2_2"><i><font color="Green" title="E28">A260</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_2_3"/><i><font color="Green" title="E26">A261</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_2_3"/><i><font color="Green" title="E27">A262</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_3_2_3"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_2_3"><i><font color="Green" title="E26">A261</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E4:20_1_1_3_2_3"/><b>then </b><i><font color="Green" title="E28">A263</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">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/><a NAME="E5:20_1_1_3_2_3"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_3_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_2"><i><font color="Green" title="E24">A250</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_2_3"><i><font color="Green" title="E27">A262</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_2_3"><i><font color="Green" title="E28">A263</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_2"><i><font color="Green" title="E23">A249</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_2"><i><font color="Green" title="E24">A250</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_2"><i><font color="Green" title="E25">A257</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:20_1_1_3"/><i><font color="Green" title="E23">A264</font></i>: 
( <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3"/><i><font color="Green" title="E24">A265</font></i>: 
(  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> or  not <font color="Maroon" title="c10">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> or  not <font color="Maroon" title="c11">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E25">A266</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_3_1"/><i><font color="Green" title="E26">A267</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_3_1"/><i><font color="Green" title="E27">A268</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_1"/><i><font color="Green" title="E28">A269</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_3_1_1"/><i><font color="Green" title="E29">A270</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_3_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_3_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_3_3_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_1_1"/><b>then </b><i><font color="Green" title="E30">A271</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</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="E5:20_1_1_3_3_1_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_1_1_2"/><i><font color="Green" title="E31">A272</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1"><i><font color="Green" title="E26">A267</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1_1"><i><font color="Green" title="E28">A269</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_3_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1_1_2"><i><font color="Green" title="E31">A272</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</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="E10:20_1_1_3_3_1_1_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_3_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1_1"><i><font color="Green" title="E28">A269</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3_1_1"><i><font color="Green" title="E29">A270</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_3_1_1"><i><font color="Green" title="E30">A271</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_3_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_2"/><i><font color="Green" title="E28">A273</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_3_1_2"/><i><font color="Green" title="E29">A274</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_3_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_3_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_3_3_1_2"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_1_2"/><b>then </b><i><font color="Green" title="E30">A275</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">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="E5:20_1_1_3_3_1_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c11">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_1_2_2"/><i><font color="Green" title="E31">A276</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_1_2_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1"><i><font color="Green" title="E26">A267</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1_2"><i><font color="Green" title="E28">A273</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_1_2_2"/><b>then </b>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</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="E4:20_1_1_3_3_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_3_3_1_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_1_2_2"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1_2_2"><i><font color="Green" title="E31">A276</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_3_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</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="E10:20_1_1_3_3_1_2_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c11">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_3_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_3_1_2"><i><font color="Green" title="E28">A273</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3_1_2"><i><font color="Green" title="E29">A274</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_3_1_2"><i><font color="Green" title="E30">A275</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_1_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3_1"><i><font color="Green" title="E27">A268</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E26">A277</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_3_2"/><i><font color="Green" title="E27">A278</font></i>: 
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_3_2"/><i><font color="Green" title="E28">A279</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_3_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_3_3_2"/><b>then </b><i><font color="Green" title="E29">A280</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">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/><a NAME="E5:20_1_1_3_3_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_2_2"/><i><font color="Green" title="E30">A281</font></i>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3"><i><font color="Green" title="E25">A266</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_2"><i><font color="Green" title="E27">A278</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">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/>
<a NAME="E4:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">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="E7:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3"><i><font color="Green" title="E22">A248</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_2_2"><i><font color="Green" title="E30">A281</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">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="E10:20_1_1_3_3_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:20_1_1_3_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_3"><i><font color="Green" title="E25">A266</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3_2"><i><font color="Green" title="E28">A279</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_3_2"><i><font color="Green" title="E29">A280</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_3_3"/><i><font color="Green" title="E27">A282</font></i>: 
<font color="Maroon" title="c11">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_3_3"/><i><font color="Green" title="E28">A283</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_3_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_3_3"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_3_3_3"/><b>then </b><i><font color="Green" title="E29">A284</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">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/><a NAME="E5:20_1_1_3_3_3"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_3_2"/><i><font color="Green" title="E30">A285</font></i>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3"><i><font color="Green" title="E25">A266</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_3"><i><font color="Green" title="E27">A282</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">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/>
<a NAME="E4:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</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="E6:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3"><i><font color="Green" title="E22">A248</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_3_3_2"><i><font color="Green" title="E30">A285</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">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="E10:20_1_1_3_3_3_2"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:20_1_1_3_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_3"><i><font color="Green" title="E25">A266</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3_3"><i><font color="Green" title="E28">A283</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_3_3"><i><font color="Green" title="E29">A284</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_3"><i><font color="Green" title="E24">A265</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_3"><i><font color="Green" title="E25">A266</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_3"><i><font color="Green" title="E26">A277</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c12">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="E7:20_1_1_3"/><i><font color="Green" title="E24">A286</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c12">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c12">d</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><a NAME="E8:20_1_1_3"/><i><font color="Green" title="E25">A287</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c12">d</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a></i>;<br/><a NAME="E9:20_1_1_3"/>
 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/>( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</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="c3">Z</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_4"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c13">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="E2:20_1_1_3_4"/><i><font color="Green" title="E26">A288</font></i>: 
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">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="c14">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="E4:20_1_1_3_4"/><i><font color="Green" title="E27">A289</font></i>: 
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font> &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_3_4"/>
not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_4_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_4_1"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_4"><i><font color="Green" title="E26">A288</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_4_1"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3_4"><i><font color="Green" title="E27">A289</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_3_4_1"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</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="E5:20_1_1_3_4_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_3_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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="E7:20_1_1_3_4"/><i><font color="Green" title="E28">A290</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font>,<font color="Maroon" title="c15">d1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>,<font color="Maroon" title="c15">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="c15">d1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</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="c3">Z</font> )</span><br/>

<a NAME="E8:20_1_1_3_4"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c15">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_4"><i><font color="Green" title="E28">A290</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="E9:20_1_1_3_4"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c15">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_4"><i><font color="Green" title="E26">A288</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:20_1_1_3_4"/><b>then </b><i><font color="Green" title="E29">A291</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</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="E11:20_1_1_3_4"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_4"><i><font color="Green" title="E28">A290</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="E12:20_1_1_3_4"/>
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</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="c3">Z</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_4"><i><font color="Green" title="E27">A289</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_3_4"><i><font color="Green" title="E29">A291</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c13">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="E11:20_1_1_3"/><i><font color="Green" title="E26">A292</font></i>: 
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font> &amp; <font color="Maroon" title="c13">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> )
 ;<br/><a NAME="E12:20_1_1_3"/>
 ex <font color="Olive" title="b1">d2</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="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">d2</font> &amp; <font color="Olive" title="b1">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_5"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c14">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="E2:20_1_1_3_5"/><i><font color="Green" title="E27">A293</font></i>: 
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">e1</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">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="c15">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="E4:20_1_1_3_5"/><i><font color="Green" title="E28">A294</font></i>: 
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">e2</font> &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_3_5"/>
not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_5_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_5_1"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">e2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_5"><i><font color="Green" title="E27">A293</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_5_1"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3_5"><i><font color="Green" title="E28">A294</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_3_5_1"/><b>then </b>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</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="E5:20_1_1_3_5_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_3_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c16">d2</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="E7:20_1_1_3_5"/><i><font color="Green" title="E29">A295</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">e1</font>,<font color="Maroon" title="c16">d2</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">e2</font>,<font color="Maroon" title="c16">d2</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="c16">d2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c16">d2</font> &amp; <font color="Maroon" title="c16">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )</span><br/>

<a NAME="E8:20_1_1_3_5"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c16">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_5"><i><font color="Green" title="E29">A295</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="E9:20_1_1_3_5"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c16">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_5"><i><font color="Green" title="E27">A293</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E10:20_1_1_3_5"/><b>then </b><i><font color="Green" title="E30">A296</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c16">d2</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="E11:20_1_1_3_5"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c16">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_5"><i><font color="Green" title="E29">A295</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="E12:20_1_1_3_5"/>
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c16">d2</font> &amp; <font color="Maroon" title="c16">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_5"><i><font color="Green" title="E28">A294</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_3_5"><i><font color="Green" title="E30">A296</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c14">d2</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="E14:20_1_1_3"/><i><font color="Green" title="E27">A297</font></i>: 
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d2</font> &amp; <font color="Maroon" title="c14">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 ;<br/><a NAME="E15:20_1_1_3"/><i><font color="Green" title="E28">A298</font></i>: 
<font color="Maroon" title="c13">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_6"/>
<font color="Maroon" title="c13">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_6"/><b>then </b><i><font color="Green" title="E29">A299</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">d1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_3_6"/><i><font color="Green" title="E30">A300</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_6_1"/><i><font color="Green" title="E31">A301</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_6_1"/><i><font color="Green" title="E32">A302</font></i>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E8:20_1_1_3"><i><font color="Green" title="E25">A287</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="E3:20_1_1_3_6_1"/><i><font color="Green" title="E33">A303</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_6_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_6_1_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_6_1_1"/><b>then </b>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_3_6_1_1"/><b>then </b><i><font color="Green" title="E34">A304</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_3_6_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_3_6_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3"><i><font color="Green" title="E19">A241</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_6_1_1"><i><font color="Green" title="E34">A304</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_6_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3"><i><font color="Green" title="E22">A248</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_6_1"><i><font color="Green" title="E32">A302</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">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/>
<a NAME="E7:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">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/>
<a NAME="E9:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E10:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_6_1"><i><font color="Green" title="E31">A301</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_6_1"><i><font color="Green" title="E33">A303</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E13:20_1_1_3_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_6"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">d1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_3_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3"><i><font color="Green" title="E19">A241</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_6"><i><font color="Green" title="E29">A299</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_6"><i><font color="Green" title="E30">A300</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><div><i><font color="Green" title="E29">A305</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_7"/><i><font color="Green" title="E30">A306</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_7"/>
 ex <font color="Olive" title="b1">d5</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">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Olive" title="b1">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Olive" title="b1">d5</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_1"><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="E2:20_1_1_3_7_1"/><i><font color="Green" title="E31">A307</font></i>: 
( <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> &amp; <font color="Maroon" title="c7">b</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="E4:20_1_1_3_7_1"/><i><font color="Green" title="E32">A308</font></i>: 
( <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c16">e2</font> &amp; <font color="Maroon" title="c13">d1</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="E5:20_1_1_3_7_1"/>
not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c16">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c16">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3_7_1"><i><font color="Green" title="E32">A308</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_7_1"><i><font color="Green" title="E31">A307</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="E4:20_1_1_3_7_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E15:20_1_1_3"><i><font color="Green" title="E28">A298</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7"><i><font color="Green" title="E30">A306</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c17">d5</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="E7:20_1_1_3_7_1"/><i><font color="Green" title="E33">A309</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font>,<font color="Maroon" title="c17">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c16">e2</font>,<font color="Maroon" title="c17">d5</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">d5</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c17">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Maroon" title="c17">d5</font> )</span><br/>

<a NAME="E8:20_1_1_3_7_1"/>
( <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c16">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c17">d5</font> &amp; <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c17">d5</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_7_1"><i><font color="Green" title="E33">A309</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="E9:20_1_1_3_7_1"/><b>then </b>
( <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c17">d5</font> &amp; <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c17">d5</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1_3_7_1"><i><font color="Green" title="E31">A307</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_7_1"><i><font color="Green" title="E32">A308</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="E10:20_1_1_3_7_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c17">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Maroon" title="c17">d5</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c15">d5</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="E4:20_1_1_3_7"/><i><font color="Green" title="E31">A310</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c15">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Maroon" title="c15">d5</font> )
 ;<br/><a NAME="E5:20_1_1_3_7"/><i><font color="Green" title="E32">A311</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3"><i><font color="Green" title="E22">A248</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_3"><i><font color="Green" title="E25">A287</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><div><i><font color="Green" title="E33">A312</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_7_2"/><i><font color="Green" title="E34">A313</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d5</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:20_1_1_3_7_2"/><i><font color="Green" title="E35">A314</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_1"/><b>then </b><i><font color="Green" title="E36">A315</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_1"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_1_1"/><i><font color="Green" title="E37">A316</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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="E7:20_1_1_3_7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c9">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/>
<a NAME="E8:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">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/>
<a NAME="E9:20_1_1_3_7_2_1_1"/><b>then </b><i><font color="Green" title="E38">A317</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">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="E10:20_1_1_3_7_2_1_1"/><i><font color="Green" title="E39">A318</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_1_1_1"/><i><font color="Green" title="E40">A319</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_1_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_7_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7_2_1_1_1"><i><font color="Green" title="E40">A319</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E11:20_1_1_3_7_2_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7_2_1_1"><i><font color="Green" title="E37">A316</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="E12:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E13:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</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="E14:20_1_1_3_7_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_3_7_2_1_1"><i><font color="Green" title="E38">A317</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_3_7_2_1_1"><i><font color="Green" title="E39">A318</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_7_2_1"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_7"><i><font color="Green" title="E32">A311</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_7_2_1"><i><font color="Green" title="E36">A315</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_2_1"/><b>then </b><i><font color="Green" title="E37">A320</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_3_7_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E7:20_1_1_3_7_2_1"/><b>then </b>
<font color="Maroon" title="c2">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_7_2_1"><i><font color="Green" title="E37">A320</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_3_7_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_7_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">d5</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_7_2_2"/><i><font color="Green" title="E36">A321</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>;<br/>
<a NAME="E2:20_1_1_3_7_2_2"/><i><font color="Green" title="E37">A322</font></i>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</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="E3:20_1_1_3_7_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">d5</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3_7"><i><font color="Green" title="E31">A310</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="E4:20_1_1_3_7_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">d5</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_7_2_2"><i><font color="Green" title="E36">A321</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_7_2_2"><i><font color="Green" title="E37">A322</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Maroon" title="c12">d</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1_3_7"><i><font color="Green" title="E31">A310</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7_2"><i><font color="Green" title="E34">A313</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_7_2"><i><font color="Green" title="E35">A314</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E5:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</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="E6:20_1_1_3_7_2"/><b>then </b><i><font color="Green" title="E36">A323</font></i>: 
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d2</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="E7:20_1_1_3_7_2"/><i><font color="Green" title="E37">A324</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_3"/><i><font color="Green" title="E38">A325</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_3"/><b>then </b><i><font color="Green" title="E39">A326</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_3_7_2_3"/><i><font color="Green" title="E40">A327</font></i>: 
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_7_2_3"><i><font color="Green" title="E39">A326</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_7_2_3"><i><font color="Green" title="E40">A327</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_3_7_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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="E8:20_1_1_3_7_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_3_7_2_3"/><b>then </b><i><font color="Green" title="E41">A328</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">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="E11:20_1_1_3_7_2_3"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7_2_3"><i><font color="Green" title="E38">A325</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="E12:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E13:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_7_2_3"><i><font color="Green" title="E40">A327</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="E14:20_1_1_3_7_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_3_7_2_3"><i><font color="Green" title="E41">A328</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E8:20_1_1_3_7_2"/><i><font color="Green" title="E38">A329</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_4"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_4"/><b>then </b><i><font color="Green" title="E39">A330</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_4"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_7"><i><font color="Green" title="E32">A311</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_3_7_2_4"/><b>then </b>
<font color="Maroon" title="c2">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c3">Z</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_7_2"><i><font color="Green" title="E37">A324</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_7_2_4"><i><font color="Green" title="E39">A330</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_3_7_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_3_7_2"/><i><font color="Green" title="E39">A331</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_5"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_5"/><b>then </b><i><font color="Green" title="E40">A332</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_5"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_7"><i><font color="Green" title="E32">A311</font></i></a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_3_7_2_5"/><b>then </b>
<font color="Maroon" title="c2">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c4">M</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_7_2"><i><font color="Green" title="E37">A324</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_7_2_5"><i><font color="Green" title="E40">A332</font></i></a>, <a class="ref" href="aff_1.html#T67" title="AFF_1:th.67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_3_7_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E10:20_1_1_3_7_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_3_7_2"><i><font color="Green" title="E36">A323</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_3_7_2"><i><font color="Green" title="E38">A329</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E11:20_1_1_3_7_2"/><b>then </b><i><font color="Green" title="E40">A333</font></i>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="txt" href="conmetr1.html#E9:20_1_1_3_7_2"><i><font color="Green" title="E39">A331</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E12:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E13:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E14:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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="E15:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c9">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/><a NAME="E16:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">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/><a NAME="E17:20_1_1_3_7_2"/><b>then </b><i><font color="Green" title="E41">A334</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">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="E18:20_1_1_3_7_2"/><i><font color="Green" title="E42">A335</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_6"/><i><font color="Green" title="E43">A336</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_7_2_6"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_7_2_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7_2_6"><i><font color="Green" title="E43">A336</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E19:20_1_1_3_7_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E11:20_1_1_3_7_2"><i><font color="Green" title="E40">A333</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="E20:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E21:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E22:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E23:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</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="E24:20_1_1_3_7_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E17:20_1_1_3_7_2"><i><font color="Green" title="E41">A334</font></i></a>, <a class="txt" href="conmetr1.html#E18:20_1_1_3_7_2"><i><font color="Green" title="E42">A335</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><a NAME="E7:20_1_1_3_7"/>
not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E15:20_1_1_3"><i><font color="Green" title="E28">A298</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_7"><i><font color="Green" title="E30">A306</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="E8:20_1_1_3_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_7"><i><font color="Green" title="E31">A310</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_7"><i><font color="Green" title="E32">A311</font></i></a>, <a class="txt" href="conmetr1.html#E6:20_1_1_3_7"><i><font color="Green" title="E33">A312</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_8"/><i><font color="Green" title="E30">A337</font></i>: 
not <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><b>then consider </b><font color="Maroon" title="c15">d5</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="E3:20_1_1_3_8"/><i><font color="Green" title="E31">A338</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c15">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>,<font color="Maroon" title="c15">d5</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><a NAME="E4:20_1_1_3_8"/><i><font color="Green" title="E32">A339</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3"><i><font color="Green" title="E22">A248</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_3"><i><font color="Green" title="E25">A287</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E5:20_1_1_3_8"/><i><font color="Green" title="E33">A340</font></i>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E6:20_1_1_3_8"/>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E7:20_1_1_3_8"/><b>then </b><i><font color="Green" title="E34">A341</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d5</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8"><i><font color="Green" title="E30">A337</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_8"><i><font color="Green" title="E31">A338</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8"><i><font color="Green" title="E32">A339</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3_8"><i><font color="Green" title="E33">A340</font></i></a></i>;<br/><a NAME="E8:20_1_1_3_8"/><i><font color="Green" title="E35">A342</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_1"/><b>then </b><i><font color="Green" title="E36">A343</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_1"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_1_1"/><i><font color="Green" title="E37">A344</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_1_1"/><b>then </b><i><font color="Green" title="E38">A345</font></i>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">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="E4:20_1_1_3_8_1_1"/><i><font color="Green" title="E39">A346</font></i>: 
( <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_1_1_1"/><i><font color="Green" title="E40">A347</font></i>: 
(  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> or  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_1_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_8_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8_1_1_1"><i><font color="Green" title="E40">A347</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E5:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_8_1_1"><i><font color="Green" title="E38">A345</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8_1_1"><i><font color="Green" title="E39">A346</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_3_8_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_3_8_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_3_8_1_1"/><b>then </b><i><font color="Green" title="E40">A348</font></i>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E11:20_1_1_3_8_1_1"/>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8_1_1"><i><font color="Green" title="E37">A344</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="E12:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">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="E13:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8_1_1"><i><font color="Green" title="E39">A346</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="E14:20_1_1_3_8_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_3_8_1_1"><i><font color="Green" title="E40">A348</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_8_1"/><b>then </b>
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8"><i><font color="Green" title="E32">A339</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_8_1"><i><font color="Green" title="E36">A343</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E5:20_1_1_3_8_1"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_3_8_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_3_8_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_3_8"/>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c15">d5</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_8_2"/><i><font color="Green" title="E36">A349</font></i>: 
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="aff_1.html#T12" title="AFF_1:th.12">AFF_1:12</a></i>;<br/>
<a NAME="E2:20_1_1_3_8_2"/><i><font color="Green" title="E37">A350</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c15">d5</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1_3_8"><i><font color="Green" title="E31">A338</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="E3:20_1_1_3_8_2"/>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</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="E4:20_1_1_3_8_2"/>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c15">d5</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_3_8_2"><i><font color="Green" title="E36">A349</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3_8_2"><i><font color="Green" title="E37">A350</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E10:20_1_1_3_8"/><b>then </b>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">d5</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3_8"><i><font color="Green" title="E34">A341</font></i></a>, <a class="txt" href="conmetr1.html#E8:20_1_1_3_8"><i><font color="Green" title="E35">A342</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E11:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font>,<font color="Maroon" title="c14">d2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1_3_8"><i><font color="Green" title="E31">A338</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E12:20_1_1_3_8"/><b>then </b><i><font color="Green" title="E36">A351</font></i>: 
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d2</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="E13:20_1_1_3_8"/><i><font color="Green" title="E37">A352</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_3"/><i><font color="Green" title="E38">A353</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_3"/><b>then </b><i><font color="Green" title="E39">A354</font></i>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_3_8_3"/><i><font color="Green" title="E40">A355</font></i>: 
( <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3_8_3"><i><font color="Green" title="E39">A354</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8_3"><i><font color="Green" title="E40">A355</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_3_8_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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="E8:20_1_1_3_8_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_3_8_3"/><b>then </b><i><font color="Green" title="E41">A356</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">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="E11:20_1_1_3_8_3"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:20_1_1_3"><i><font color="Green" title="E24">A286</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8_3"><i><font color="Green" title="E38">A353</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="E12:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E13:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8_3"><i><font color="Green" title="E40">A355</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="E14:20_1_1_3_8_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E10:20_1_1_3_8_3"><i><font color="Green" title="E41">A356</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E14:20_1_1_3_8"/><i><font color="Green" title="E38">A357</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_4"/><i><font color="Green" title="E39">A358</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_4"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8"><i><font color="Green" title="E32">A339</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_8_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_3_8"><i><font color="Green" title="E37">A352</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8_4"><i><font color="Green" title="E39">A358</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E15:20_1_1_3_8"/><i><font color="Green" title="E39">A359</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_5"/><i><font color="Green" title="E40">A360</font></i>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_5"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="txt" href="conmetr1.html#E4:20_1_1_3_8"><i><font color="Green" title="E32">A339</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_8_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="txt" href="conmetr1.html#E13:20_1_1_3_8"><i><font color="Green" title="E37">A352</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8_5"><i><font color="Green" title="E40">A360</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E16:20_1_1_3_8"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d2</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E11:20_1_1_3"><i><font color="Green" title="E26">A292</font></i></a>, <a class="txt" href="conmetr1.html#E12:20_1_1_3_8"><i><font color="Green" title="E36">A351</font></i></a>, <a class="txt" href="conmetr1.html#E14:20_1_1_3_8"><i><font color="Green" title="E38">A357</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E17:20_1_1_3_8"/><b>then </b><i><font color="Green" title="E40">A361</font></i>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E14:20_1_1_3"><i><font color="Green" title="E27">A297</font></i></a>, <a class="txt" href="conmetr1.html#E15:20_1_1_3_8"><i><font color="Green" title="E39">A359</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E18:20_1_1_3_8"/><i><font color="Green" title="E41">A362</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_6"/><i><font color="Green" title="E42">A363</font></i>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:20_1_1_3_8_6"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_3"><i><font color="Green" title="E20">A242</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_8_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E5:20_1_1_3"><i><font color="Green" title="E23">A264</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_3_8_6"><i><font color="Green" title="E42">A363</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E19:20_1_1_3_8"/>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="txt" href="conmetr1.html#E17:20_1_1_3_8"><i><font color="Green" title="E40">A361</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E20:20_1_1_3_8"/><b>then </b>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E21:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">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="E22:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c9">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/><a NAME="E23:20_1_1_3_8"/><b>then </b>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">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/><a NAME="E24:20_1_1_3_8"/><b>then </b><i><font color="Green" title="E42">A364</font></i>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">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="E25:20_1_1_3_8"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E17:20_1_1_3_8"><i><font color="Green" title="E40">A361</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="E26:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E27:20_1_1_3_8"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E28:20_1_1_3_8"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E29:20_1_1_3_8"/><b>then </b>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1_3"><i><font color="Green" title="E21">A243</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="E30:20_1_1_3_8"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="conmetr1.html#E18:20_1_1_3_8"><i><font color="Green" title="E41">A362</font></i></a>, <a class="txt" href="conmetr1.html#E24:20_1_1_3_8"><i><font color="Green" title="E42">A364</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E18:20_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E16:20_1_1_3"><i><font color="Green" title="E29">A305</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E6:20_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E4:20_1_1"><i><font color="Green" title="E18">A239</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_1"/>
<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#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:20"/>
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a>  implies <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_2"/><i><font color="Green" title="E14">A365</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a> </span><br/>

<a NAME="E2:20_2"/><b>then </b>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR7" title="AFF_2:NR.7">satisfies_TDES</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T26" title="AFF_2:th.26">AFF_2:26</a></i>;<br/>
<a NAME="E3:20_2"/><b>then </b>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR8" title="AFF_2:NR.8">satisfies_TDES_1</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T17" title="AFF_2:th.17">AFF_2:17</a></i>;<br/>
<a NAME="E4:20_2"/><b>then </b>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR12" title="AFF_2:NR.12">satisfies_des_1</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T27" title="AFF_2:th.27">AFF_2:27</a></i>;<br/>
<a NAME="E5:20_2"/><b>then </b>
<font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR11" title="AFF_2:NR.11">satisfies_des</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T21" title="AFF_2:th.21">AFF_2:21</a></i>;<br/>
<a NAME="E6:20_2"/><b>then </b><i><font color="Green" title="E15">A366</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR1" title="CONMETR1:NR.1">satisfies_minor_SCH</a> 
 
<b>by </b><i><a class="ref" href="conmetr1.html#T6" target="_self" title="CONMETR1:th.6">Th6</a></i>;<br/>
<a NAME="E7:20_2"/>
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR2" title="CONMETR1:NR.2">satisfies_major_SCH</a> 
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:20_2"><i><font color="Green" title="E14">A365</font></i></a>, <a class="ref" href="conmetr1.html#T7" target="_self" title="CONMETR1:th.7">Th7</a></i>;<br/>
<b>hence </b><a NAME="E8:20_2"/>
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a> 
 <b>by </b><i><a class="txt" href="conmetr1.html#E6:20_2"><i><font color="Green" title="E15">A366</font></i></a>, <a class="ref" href="conmetr1.html#T2" target="_self" title="CONMETR1:th.2">Th2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a>  iff <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR3" title="CONMETR1:NR.3">satisfies_SCH</a>  )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20"><i><font color="Green" title="E13">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
