<?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">p</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d</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">p</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">d</font> holds <br/> not  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">d</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d</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">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font> &amp; <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="c5">c</font>,<font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font> implies  not  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:23"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E2:23"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E3:23"/><span class="lab"><font color="Green" title="E14">A3</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="c5">c</font>,<font color="Maroon" title="c6">d</font>
 <span class="kw">and </span><br/><a NAME="E4:23"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</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#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d</font></span><br/>

<span class="kw">assume </span><a NAME="E5:23"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d</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="E6:23"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a></span>;<br/>
<a NAME="E7:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E8:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A6</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</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/>
<span class="kw">consider </span><font color="Maroon" title="c7">b9</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="E10:23"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">b9</font>
 <span class="kw">and </span><br/><a NAME="E11:23"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E12:23"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:23_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</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="E2:23_1"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E3:23_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:23_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</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="E13:23"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:23_2"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b9</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="E2:23_2"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:23_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E1:23_2"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:23_2"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E5:23_2"/><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">p</font>,<font color="Maroon" title="c3">a</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/>
<span class="kw">hence </span><a NAME="E6:23_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</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="E14:23"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E15:23"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E16:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A12</font></span>: 
<font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">b</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="E17:23"/><span class="lab"><font color="Green" title="E23">A13</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:23_3"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</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="E2:23_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E3:23_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</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="E4:23_3"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E5:23_3"/><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">p</font>,<font color="Maroon" title="c3">a</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/>
<span class="kw">hence </span><a NAME="E6:23_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</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="E18:23"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:23_4"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b9</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="E2:23_4"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E23">A13</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E3:23_4"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:23_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</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>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">b99</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="E20:23"/><span class="lab"><font color="Green" title="E24">A14</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">b99</font>
 <span class="kw">and </span><br/><a NAME="E21:23"/><span class="lab"><font color="Green" title="E25">A15</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">b99</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E22">A12</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E22:23"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E23:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A16</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E24:23"/>
<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="c3">a</font>,<font color="Maroon" title="c7">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E23">A13</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E25:23"/><span class="kw">then </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="c4">b</font>,<font color="Maroon" title="c8">b99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:23"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E26:23"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">b99</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">b99</font>,<font color="Maroon" title="c3">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T7" title="DIRAF:th.7">DIRAF:7</a></span>;<br/>
<a NAME="E27:23"/><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="c3">a</font>,<font color="Maroon" title="c8">b99</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">b99</font>,<font color="Maroon" title="c3">a</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="E28:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A17</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">b99</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="E29:23"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">b99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E30:23"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">b99</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="E31:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A18</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">b99</font>,<font color="Maroon" title="c2">p</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="E32:23"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">b99</font>,<font color="Maroon" title="c3">a</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">hence </span><a NAME="E33:23"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E31:23"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="txt" href="#E23:23"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E28:23"><span class="lab"><font color="Green" title="E27">A17</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>
