<?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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">d</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">d</font>,<font color="Olive" title="b3">a</font> &amp; <font color="Olive" title="b4">c</font>,<font color="Olive" title="b2">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b</font>,<font color="Olive" title="b3">a</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">b</font> &amp; not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b5">b</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="b4">c</font> holds <br/> <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">d</font>, <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">b</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="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">a</font> &amp; <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font> &amp; <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="c2">p</font>,<font color="Maroon" title="c6">b</font> &amp; not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</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="c5">c</font> implies  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:29"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">a</font>
 <span class="kw">and </span><br/><a NAME="E2:29"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font>
 <span class="kw">and </span><br/><a NAME="E3:29"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<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="c2">p</font>,<font color="Maroon" title="c6">b</font>
 <span class="kw">and </span><br/><a NAME="E4:29"/><span class="lab"><font color="Green" title="E14">A4</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="c4">a</font>,<font color="Maroon" title="c6">b</font>
 <span class="kw">and </span><br/><a NAME="E5:29"/><span class="lab"><font color="Green" title="E15">A5</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font></span><br/>

<a NAME="E6:29"/><span class="lab"><font color="Green" title="E16">A6</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="c3">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:29_1"/><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:29_1"/>
<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="c6">b</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></span>;<br/>
<a NAME="E3:29_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E5:29"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E1:29_1"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E4:29_1"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">a</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></span>;<br/>
<a NAME="E5:29_1"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">a</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:29_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E7:29"/>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></span>;<br/>
<a NAME="E8:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A8</font></span>: 
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></span>;<br/>
<a NAME="E9:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A9</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:29_2"/><span class="lab"><font color="Green" title="E19">A10</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">d</font>,<font color="Maroon" title="c5">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:29_2_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c5">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:29_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A11</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/>
<a NAME="E3:29_2_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/>
<a NAME="E4:29_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A12</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c6">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:29"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E9:29"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E2:29_2_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/>
<a NAME="E5:29_2_1"/><span class="lab"><font color="Green" title="E22">A13</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/>
<a NAME="E6:29_2_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:29_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E6:29"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E4:29_2_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="txt" href="#E5:29_2_1"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:29_2"/><span class="lab"><font color="Green" title="E20">A14</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font></span><br/><a NAME="E3:29_2"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E4:29_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E5:29_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A15</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></span>;<br/><a NAME="E6:29_2"/><span class="lab"><font color="Green" title="E22">A16</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">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E7:29_2"/>
<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></span>;<br/><a NAME="E8:29_2"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29_2"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E5:29_2"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E6:29_2"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E1:29_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="ref" href="pasch.html#T22" target="_self" title="PASCH:th.22">Th22</a></span>;<br/><a NAME="E9:29_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A17</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">p</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="E10:29_2"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></span>;<br/><a NAME="E11:29_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c4">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E9:29_2"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="diraf.html#T18" title="DIRAF:th.18">DIRAF:18</a></span>;<br/><a NAME="E12:29_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></span>;<br/><a NAME="E13:29_2"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></span>;<br/><a NAME="E14:29_2"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></span>;<br/><a NAME="E15:29_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A18</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E16:29_2"/><span class="lab"><font color="Green" title="E25">A19</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E17:29_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">b</font>,<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="#E8:29"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E18:29_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E15:29_2"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E16:29_2"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><span class="kw">hence </span><a NAME="E19:29_2"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T14" title="DIRAF:th.14">DIRAF:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E11:29"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
