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

<span class="kw">let </span><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">a9</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> holds <br/>( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">a9</font>, <font color="Maroon" title="c6">b9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> &amp; <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">a9</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">b9</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font> implies ( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b9</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<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">a9</font>
 <span class="kw">and </span><br/><a NAME="E3:14"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">b9</font>
 <span class="kw">and </span><br/><a NAME="E4:14"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b9</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font> )</span><br/>

<a NAME="E5:14"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">a2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E7:14"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>
 <span class="kw">and </span><br/><a NAME="E8:14"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></span>;<br/>
<a NAME="E9:14"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><span class="kw"> such that </span><br/><a NAME="E11:14"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>
 <span class="kw">and </span><br/><a NAME="E12:14"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E13:14"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E14:14"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E15:14"/><span class="kw">then </span>
<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c2">o</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E16:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E17:14"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E18:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A12</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<a NAME="E19:14"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:14_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></span>;<br/>
<a NAME="E4:14_1"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c2">o</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c4">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a>, <a class="ref" href="diraf.html#T33" title="DIRAF:th.33">DIRAF:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E20:14"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E21:14"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E22:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A14</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<a NAME="E23:14"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_2"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E2:14_2"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_2"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E2:14_2"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E1:14_2"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E24:14"/>
<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E25:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A18</font></span>: 
<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></span>;<br/>
<a NAME="E26:14"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E27:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A19</font></span>: 
<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="diraf.html#T23" title="DIRAF:th.23">DIRAF:23</a></span>;<br/>
<a NAME="E28:14"/><span class="lab"><font color="Green" title="E32">A20</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E29:14"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E30:14"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E31:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A21</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<a NAME="E32:14"/><span class="lab"><font color="Green" title="E34">A22</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E33:14"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E34:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A23</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c6">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="txt" href="#E32:14"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/>
<a NAME="E35:14"/><span class="kw">then </span>
<font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c5">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="papdesaf.html#T7" target="_self" title="PAPDESAF:th.7">Th12</a></span>;<br/>
<a NAME="E36:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A24</font></span>: 
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E37:14"/>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E34:14"><span class="lab"><font color="Green" title="E35">A23</font></span></a>, <a class="ref" href="papdesaf.html#T7" target="_self" title="PAPDESAF:th.7">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E38:14"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font></span><br/>

<a NAME="E39:14"/>
<font color="Maroon" title="c7">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E40:14"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E36">A24</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
