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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="conaffm.html#NR2" title="CONAFFM:NR.2">AH_holds_in</a> <font color="Maroon" title="c1">X</font> implies  <a href="conmetr.html#NR5" title="CONMETR:NR.5">TDES_holds_in</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E15">A1</font></i>: 
 <a href="conaffm.html#NR2" title="CONAFFM:NR.2">AH_holds_in</a> <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">  <a href="conmetr.html#NR5" title="CONMETR:NR.5">TDES_holds_in</a> <font color="Maroon" title="c1">X</font></span><br/>

<b>let </b><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">CONMETR:def 5</a> <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">a</font>, <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">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="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">c</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">c1</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b1</font>,<font color="Olive" title="b1">a</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">c1</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">c</font> &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b6">c1</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b6">c1</font></span><br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> implies <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> )</span><br/>













<b>assume </b><a NAME="E2:13"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">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="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font></span><br/>

<b>consider </b><font color="Maroon" title="c9">c2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:13"/><i><font color="Green" title="E17">A3</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">c2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">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="E6:13"/><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">e1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">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="E8:13"/><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c11">e2</font> &amp; <font color="Maroon" title="c9">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">o'</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c13">a'</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c14">a1'</font> = <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c15">b'</font> = <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c16">b1'</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c17">c'</font> = <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c18">c1'</font> = <font color="Maroon" title="c8">c1</font>, <font color="Maroon" title="c19">c2'</font> = <font color="Maroon" title="c9">c2</font>, <font color="Maroon" title="c20">e1'</font> = <font color="Maroon" title="c10">e1</font>, <font color="Maroon" title="c21">e2'</font> = <font color="Maroon" title="c11">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E10:13"/><i><font color="Green" title="E20">A6</font></i>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c14">a1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">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="E4:13_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">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="E5:13_1"/><b>then </b><i><font color="Green" title="E21">A7</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:13_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">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="E9:13_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:13_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E5:13_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:13_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:13_1"/><b>then </b><i><font color="Green" title="E22">A8</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:13_1"/><b>then </b><i><font color="Green" title="E23">A9</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c12">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="E14:13_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E12:13_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E15:13_1"/><b>then </b>
<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c12">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">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="E16:13_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">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="E17:13_1"/><b>then </b><i><font color="Green" title="E24">A10</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E18:13_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:13_1"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E17:13_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E20:13_1"/><b>then </b><i><font color="Green" title="E25">A11</font></i>: 
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E21:13_1"/>
<font color="Maroon" title="c13">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">b'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_1"/>
<font color="Maroon" title="c13">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">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="E2:13_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">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>hence </b><a NAME="E3:13_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E22:13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E13:13_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="conmetr.html#E20:13_1"><i><font color="Green" title="E25">A11</font></i></a>, <a class="ref" href="aff_1.html#T18" title="AFF_1:th.18">AFF_1:18</a></i>;<br/>
<a NAME="E23:13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">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="E24:13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E21">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_2"/><i><font color="Green" title="E22">A13</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font></span><br/><a NAME="E2:13_2"/>
not <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c20">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c21">e2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_1"/>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c20">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c21">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="E2:13_2_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c11">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_1"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c11">e2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_1"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c11">e2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:13_2_1"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:13_2_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:13_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">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="E9:13_2_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_1"/><b>then </b><i><font color="Green" title="E23">A14</font></i>: 
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:13_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c16">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="E13:13_2_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:13_2_1"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:13_2_1"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E10:13_2_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E16:13_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>then consider </b><font color="Maroon" title="c22">b2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E4:13_2"/><i><font color="Green" title="E23">A15</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c20">e1'</font>,<font color="Maroon" title="c22">b2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c21">e2'</font>,<font color="Maroon" title="c22">b2'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">b2</font> = <font color="Maroon" title="c22">b2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E6:13_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">e1</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:13_2"><i><font color="Green" title="E23">A15</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E7:13_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:13_2"/><b>then </b><i><font color="Green" title="E24">A16</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E6:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E9:13_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c11">e2</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:13_2"><i><font color="Green" title="E23">A15</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E10:13_2"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c11">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E11:13_2"/><b>then </b><i><font color="Green" title="E25">A17</font></i>: 
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E8:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><b>consider </b><font color="Maroon" title="c24">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="E13:13_2"/><i><font color="Green" title="E26">A18</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c24">e1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/><b>consider </b><font color="Maroon" title="c25">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="E15:13_2"/><i><font color="Green" title="E27">A19</font></i>: 
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c25">e2</font> &amp; <font color="Maroon" title="c9">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c26">e1'</font> = <font color="Maroon" title="c24">e1</font>, <font color="Maroon" title="c27">e2'</font> = <font color="Maroon" title="c25">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E17:13_2"/>
not <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c27">e2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_2"/>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c2'</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="E2:13_2_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c24">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c25">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_2"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c25">e2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E13:13_2"><i><font color="Green" title="E26">A18</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E15:13_2"><i><font color="Green" title="E27">A19</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:13_2_2"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_2"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c12">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="E7:13_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">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="E8:13_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">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="E9:13_2_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_2"/><b>then </b><i><font color="Green" title="E28">A20</font></i>: 
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_2_2"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:13_2_2"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">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="E13:13_2_2"/><b>then </b>
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E14:13_2_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E10:13_2_2"><i><font color="Green" title="E28">A20</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:13_2_2"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:13_2_2"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E17:13_2_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E18:13_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>then consider </b><font color="Maroon" title="c28">a2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E19:13_2"/><i><font color="Green" title="E28">A21</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c28">a2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c27">e2'</font>,<font color="Maroon" title="c28">a2'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c29">a2</font> = <font color="Maroon" title="c28">a2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E21:13_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c24">e1</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E19:13_2"><i><font color="Green" title="E28">A21</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E22:13_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c24">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E23:13_2"/><b>then </b><i><font color="Green" title="E29">A22</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E13:13_2"><i><font color="Green" title="E26">A18</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E24:13_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c25">e2</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E19:13_2"><i><font color="Green" title="E28">A21</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E25:13_2"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c25">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E26:13_2"/><b>then </b><i><font color="Green" title="E30">A23</font></i>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E15:13_2"><i><font color="Green" title="E27">A19</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E27:13_2"/><i><font color="Green" title="E31">A24</font></i>: 
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E11:13_2"><i><font color="Green" title="E25">A17</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E28:13_2"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E29:13_2"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">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="E30:13_2"/><b>then </b><i><font color="Green" title="E32">A25</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E31:13_2"/><i><font color="Green" title="E33">A26</font></i>: 
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E26:13_2"><i><font color="Green" title="E30">A23</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E32:13_2"/><i><font color="Green" title="E34">A27</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_3"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">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="E2:13_2_3"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">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="E5:13_2_3"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:13_2_3"/><b>then </b><i><font color="Green" title="E35">A28</font></i>: 
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_2_3"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:13_2_3"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E9:13_2_3"/><b>then </b>
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:13_2_3"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E6:13_2_3"><i><font color="Green" title="E35">A28</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:13_2_3"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:13_2_3"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E13:13_2_3"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E14:13_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><a NAME="E33:13_2"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_4"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">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="E2:13_2_4"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c15">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">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="E5:13_2_4"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c15">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="E6:13_2_4"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">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="E7:13_2_4"/><b>then </b><i><font color="Green" title="E35">A29</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:13_2_4"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13_2_4"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">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="E10:13_2_4"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:13_2_4"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E7:13_2_4"><i><font color="Green" title="E35">A29</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:13_2_4"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:13_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E34:13_2"/><b>then </b><i><font color="Green" title="E35">A30</font></i>: 
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="conmetr.html#E4:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr.html#E8:13_2"><i><font color="Green" title="E24">A16</font></i></a>, <a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green" title="E29">A22</font></i></a>, <a class="txt" href="conmetr.html#E27:13_2"><i><font color="Green" title="E31">A24</font></i></a>, <a class="txt" href="conmetr.html#E30:13_2"><i><font color="Green" title="E32">A25</font></i></a>, <a class="txt" href="conmetr.html#E31:13_2"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="conmetr.html#E32:13_2"><i><font color="Green" title="E34">A27</font></i></a>, <a class="ref" href="conaffm.html#D2" title="CONAFFM:def.2">CONAFFM:def 2</a></i>;<br/><b>consider </b><font color="Maroon" title="c30">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="E36:13_2"/><i><font color="Green" title="E36">A31</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c30">e1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/><b>consider </b><font color="Maroon" title="c31">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="E38:13_2"/><i><font color="Green" title="E37">A32</font></i>: 
( <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c31">e2</font> &amp; <font color="Maroon" title="c9">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c31">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c32">e1'</font> = <font color="Maroon" title="c30">e1</font>, <font color="Maroon" title="c33">e2'</font> = <font color="Maroon" title="c31">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E40:13_2"/>
not <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c32">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c33">e2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_5"/>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c32">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c33">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="E2:13_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c31">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_5"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c31">e2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E36:13_2"><i><font color="Green" title="E36">A31</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_5"/><b>then </b>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E38:13_2"><i><font color="Green" title="E37">A32</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:13_2_5"/><b>then </b>
<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_5"/><b>then </b>
<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c12">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="E7:13_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font>,<font color="Maroon" title="c12">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="E8:13_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font>,<font color="Maroon" title="c14">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="E9:13_2_5"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">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="E10:13_2_5"/><b>then </b><i><font color="Green" title="E38">A33</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:13_2_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c18">c1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:13_2_5"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:13_2_5"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">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="E14:13_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:13_2_5"/><b>then </b><i><font color="Green" title="E39">A34</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E10:13_2_5"><i><font color="Green" title="E38">A33</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:13_2_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c14">a1'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:13_2_5"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">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="E18:13_2_5"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">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="E19:13_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:13_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E15:13_2_5"><i><font color="Green" title="E39">A34</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:13_2_5"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:13_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E23:13_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">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="E24:13_2_5"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">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="E25:13_2_5"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E26:13_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E27:13_2_5"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E28:13_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>then consider </b><font color="Maroon" title="c34">a3'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E42:13_2"/><i><font color="Green" title="E38">A35</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c32">e1'</font>,<font color="Maroon" title="c34">a3'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">c2'</font>,<font color="Maroon" title="c33">e2'</font>,<font color="Maroon" title="c34">a3'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c35">a3</font> = <font color="Maroon" title="c34">a3'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E44:13_2"/><i><font color="Green" title="E39">A36</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_6"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_6"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c30">e1</font>,<font color="Maroon" title="c35">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E42:13_2"><i><font color="Green" title="E38">A35</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_2_6"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_6"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">a3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E36:13_2"><i><font color="Green" title="E36">A31</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E45:13_2"/><i><font color="Green" title="E40">A37</font></i>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c35">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_7"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c31">e2</font>,<font color="Maroon" title="c35">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E42:13_2"><i><font color="Green" title="E38">A35</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_2_7"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c31">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c35">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_7"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c35">a3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E38:13_2"><i><font color="Green" title="E37">A32</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E46:13_2"/><i><font color="Green" title="E41">A38</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_8"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_8"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E2:13_2_8"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E47:13_2"/><i><font color="Green" title="E42">A39</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c23">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_9"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_9"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E2:13_2_9"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E8:13_2"><i><font color="Green" title="E24">A16</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E48:13_2"/><i><font color="Green" title="E43">A40</font></i>: 
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c23">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_10"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_10_1"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">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="E2:13_2_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E2:13_2_10"/><b>then </b>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c23">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E11:13_2"><i><font color="Green" title="E25">A17</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_10"/>
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c23">b2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</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="E49:13_2"/><i><font color="Green" title="E44">A41</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_11"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_11"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_11_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">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="E2:13_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">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>hence </b><a NAME="E3:13_2_11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E2:13_2_11"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:13_2_11"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:13_2_11"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c14">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:13_2_11"/><b>then </b><i><font color="Green" title="E45">A42</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_11"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E7:13_2_11"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E5:13_2_11"><i><font color="Green" title="E45">A42</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</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="E50:13_2"/><i><font color="Green" title="E45">A43</font></i>: 
<font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c35">a3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E45:13_2"><i><font color="Green" title="E40">A37</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E51:13_2"/><i><font color="Green" title="E46">A44</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_12"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">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="E2:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">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="E4:13_2_12"/><b>then </b><i><font color="Green" title="E47">A45</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:13_2_12"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">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="E8:13_2_12"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13_2_12"/><b>then </b><i><font color="Green" title="E48">A46</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E4:13_2_12"><i><font color="Green" title="E47">A45</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E10:13_2_12"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c14">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">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="E13:13_2_12"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E14:13_2_12"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E9:13_2_12"><i><font color="Green" title="E48">A46</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:13_2_12"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:13_2_12"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:13_2_12"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c12">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="E18:13_2_12"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">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="E19:13_2_12"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E20:13_2_12"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E21:13_2_12"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E22:13_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><a NAME="E52:13_2"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_13"/><i><font color="Green" title="E47">A47</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">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="E2:13_2_13"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_2_13"/><b>then </b>
( <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font> &amp; <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c16">b1'</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:13_2_13"/><b>then </b>
( <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> &amp; <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">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="E5:13_2_13"/><b>then </b><i><font color="Green" title="E48">A48</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_13"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:13_2_13"><i><font color="Green" title="E47">A47</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:13_2_13"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E5:13_2_13"><i><font color="Green" title="E48">A48</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:13_2_13"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:13_2_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c15">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E11:13_2_13"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c15">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="E12:13_2_13"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">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="E13:13_2_13"/><b>then </b><i><font color="Green" title="E49">A49</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E14:13_2_13"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:13_2_13"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">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="E16:13_2_13"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E17:13_2_13"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E13:13_2_13"><i><font color="Green" title="E49">A49</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E18:13_2_13"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:13_2_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E20:13_2_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E21:13_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E53:13_2"/><b>then </b><i><font color="Green" title="E47">A50</font></i>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c35">a3</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="conmetr.html#E44:13_2"><i><font color="Green" title="E39">A36</font></i></a>, <a class="txt" href="conmetr.html#E46:13_2"><i><font color="Green" title="E41">A38</font></i></a>, <a class="txt" href="conmetr.html#E47:13_2"><i><font color="Green" title="E42">A39</font></i></a>, <a class="txt" href="conmetr.html#E48:13_2"><i><font color="Green" title="E43">A40</font></i></a>, <a class="txt" href="conmetr.html#E49:13_2"><i><font color="Green" title="E44">A41</font></i></a>, <a class="txt" href="conmetr.html#E50:13_2"><i><font color="Green" title="E45">A43</font></i></a>, <a class="txt" href="conmetr.html#E51:13_2"><i><font color="Green" title="E46">A44</font></i></a>, <a class="ref" href="conaffm.html#D2" title="CONAFFM:def.2">CONAFFM:def 2</a></i>;<br/><a NAME="E54:13_2"/><i><font color="Green" title="E48">A51</font></i>: 
<font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c35">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_14"/><i><font color="Green" title="E49">A52</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_14_1"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="E2:13_2_14_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E2:13_2_14"/>
<font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E34:13_2"><i><font color="Green" title="E35">A30</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:13_2_14"/><b>then </b>
<font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:13_2_14"><i><font color="Green" title="E49">A52</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_14"/><b>then </b>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<b>hence </b><a NAME="E5:13_2_14"/>
<font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c35">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E10:13"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="conmetr.html#E53:13_2"><i><font color="Green" title="E47">A50</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</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="E55:13_2"/><i><font color="Green" title="E49">A53</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c28">a2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c28">a2'</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="E2:13_2_15"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c23">b2</font>,<font color="Maroon" title="c29">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_2_15"/><b>then </b><i><font color="Green" title="E50">A54</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c23">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_2_15"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">b2</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="E2:13_2_15_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">c2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:13_2"><i><font color="Green" title="E25">A17</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:13_2_15_1"/><b>then </b><i><font color="Green" title="E51">A55</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:13_2_15_1"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:13_2_15_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">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="E6:13_2_15_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:13_2_15_1"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E3:13_2_15_1"><i><font color="Green" title="E51">A55</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:13_2_15_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:13_2_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E11:13_2_15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E5:13_2_15"/><b>then </b><i><font color="Green" title="E51">A56</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:13_2"><i><font color="Green" title="E24">A16</font></i></a>, <a class="txt" href="conmetr.html#E3:13_2_15"><i><font color="Green" title="E50">A54</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:13_2_15"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15_2"/><i><font color="Green" title="E52">A57</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">a2</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="E2:13_2_15_2"/>
<font color="Maroon" title="c9">c2</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:13_2_15_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr.html#E31:13_2"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="conmetr.html#E1:13_2_15_2"><i><font color="Green" title="E52">A57</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:13_2_15_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E5:13_2_15_2"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_15_2"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E7:13_2_15_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E8:13_2_15_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>
<a NAME="E7:13_2_15"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green" title="E29">A22</font></i></a>, <a class="txt" href="conmetr.html#E5:13_2_15"><i><font color="Green" title="E51">A56</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E8:13_2_15"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:13_2_15"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_15"/><b>then </b><i><font color="Green" title="E52">A58</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c12">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="E11:13_2_15"/><i><font color="Green" title="E53">A59</font></i>: 
<font color="Maroon" title="c13">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">b'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15_3"/>
<font color="Maroon" title="c13">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">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="E2:13_2_15_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_15_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E12:13_2_15"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E13:13_2_15"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E10:13_2_15"><i><font color="Green" title="E52">A58</font></i></a>, <a class="txt" href="conmetr.html#E11:13_2_15"><i><font color="Green" title="E53">A59</font></i></a>, <a class="ref" href="aff_1.html#T18" title="AFF_1:th.18">AFF_1:18</a></i>;<br/>
<b>hence </b><a NAME="E14:13_2_15"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E56:13_2"/><i><font color="Green" title="E50">A60</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c28">a2'</font>,<font color="Maroon" title="c34">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_16"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:13_2_16"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green" title="E29">A22</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:13_2_16"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">a3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E44:13_2"><i><font color="Green" title="E39">A36</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:13_2_16"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">a2</font>,<font color="Maroon" title="c35">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E5:13_2_16"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c28">a2'</font>,<font color="Maroon" title="c34">a3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E57:13_2"/>
<font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c28">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c34">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_17"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_17"/>
<font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c34">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c28">a2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E54:13_2"><i><font color="Green" title="E48">A51</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:13_2_17"/>
<font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c28">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">b2'</font>,<font color="Maroon" title="c34">a3'</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="E58:13_2"/><b>then </b><i><font color="Green" title="E51">A61</font></i>: 
<font color="Maroon" title="c28">a2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c34">a3'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E55:13_2"><i><font color="Green" title="E49">A53</font></i></a>, <a class="txt" href="conmetr.html#E56:13_2"><i><font color="Green" title="E50">A60</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E59:13_2"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_18"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_18"/>
<font color="Maroon" title="c9">c2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_18_1"/>
<font color="Maroon" title="c9">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">a2</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="E2:13_2_18_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green" title="E29">A22</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:13_2_18_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_2_18_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:13_2_18_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c12">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="E6:13_2_18_1"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c12">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="E7:13_2_18_1"/><b>then </b>
<font color="Maroon" title="c12">o'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E8:13_2_18_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13_2_18_1"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E10:13_2_18_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>
<a NAME="E2:13_2_18"/><b>then </b>
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E31:13_2"><i><font color="Green" title="E33">A26</font></i></a>, <a class="txt" href="conmetr.html#E45:13_2"><i><font color="Green" title="E40">A37</font></i></a>, <a class="txt" href="conmetr.html#E58:13_2"><i><font color="Green" title="E51">A61</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:13_2_18"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:13_2_18"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">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="E5:13_2_18"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</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="E60:13_2"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">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><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3"/><i><font color="Green" title="E22">A62</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font></span><br/><a NAME="E2:13_3"/><b>then </b><i><font color="Green" title="E23">A63</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E3:13_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E4:13_3"/><b>then </b>
<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">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="E5:13_3"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">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="E6:13_3"/><b>then </b><i><font color="Green" title="E24">A64</font></i>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E7:13_3"/><i><font color="Green" title="E25">A65</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">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="E2:13_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">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>hence </b><a NAME="E3:13_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E8:13_3"/><i><font color="Green" title="E26">A66</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3_2"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">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="E2:13_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E9:13_3"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E6:13_3"><i><font color="Green" title="E24">A64</font></i></a>, <a class="txt" href="conmetr.html#E7:13_3"><i><font color="Green" title="E25">A65</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E10:13_3"/><b>then </b>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E8:13_3"><i><font color="Green" title="E26">A66</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E11:13_3"/><b>then </b>
<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E12:13_3"/><b>then </b>
<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c14">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c18">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="E13:13_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E14:13_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c18">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="E15:13_3"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E16:13_3"/><b>then </b><i><font color="Green" title="E27">A67</font></i>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E17:13_3"/>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E18:13_3"/><b>then </b>
<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">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="E19:13_3"/><b>then </b><i><font color="Green" title="E28">A68</font></i>: 
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><div><i><font color="Green" title="E29">A69</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_3"/>
<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font></span><br/><a NAME="E2:13_3_3"/><b>then </b>
<font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E3:13_3_3"/><b>then </b>
<font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a1'</font>,<font color="Maroon" title="c18">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="E4:13_3_3"/><b>then </b><i><font color="Green" title="E30">A70</font></i>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E5:13_3_3"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_3"><i><font color="Green" title="E22">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E6:13_3_3"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E7:13_3"><i><font color="Green" title="E25">A65</font></i></a>, <a class="txt" href="conmetr.html#E4:13_3_3"><i><font color="Green" title="E30">A70</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</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="13_3_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_4"/><i><font color="Green" title="E30">A71</font></i>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font></span><br/><a NAME="E2:13_3_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c13">a'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13_3"><i><font color="Green" title="E23">A63</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E3:13_3_4"/><b>then </b>
<font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c15">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c'</font>,<font color="Maroon" title="c13">a'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E4:13_3_4"/><b>then </b>
<font color="Maroon" title="c15">b'</font>,<font color="Maroon" title="c17">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a'</font>,<font color="Maroon" title="c17">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="E5:13_3_4"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>hence </b><a NAME="E6:13_3_4"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="conmetr.html#E8:13_3"><i><font color="Green" title="E26">A66</font></i></a>, <a class="txt" href="conmetr.html#E1:13_3_4"><i><font color="Green" title="E30">A71</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</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="E22:13_3"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E16:13_3"><i><font color="Green" title="E27">A67</font></i></a>, <a class="txt" href="conmetr.html#E19:13_3"><i><font color="Green" title="E28">A68</font></i></a>, <a class="txt" href="conmetr.html#E20:13_3"><i><font color="Green" title="E29">A69</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</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="E13:13"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E11:13"><i><font color="Green" title="E21">A12</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>
