<?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> 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;  <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="b3">b</font> holds <br/> ex <font color="Olive" title="b5">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">x</font>,<font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">x</font>,<font color="Olive" title="b4">c</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> 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;  <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="c4">b</font> implies  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">a</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="Olive" title="b1">x</font>,<font color="Maroon" title="c5">c</font> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27"/><span class="lab"><font color="Green" title="E16">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="E2:27"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <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="c4">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">a</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="Olive" title="b1">x</font>,<font color="Maroon" title="c5">c</font> )</span><br/>

<a NAME="E3:27"/><span class="lab"><font color="Green" title="E18">A3</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">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E4:27"/><span class="lab"><font color="Green" title="E19">A4</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="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<a NAME="E5:27"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">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="#E2:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a></span>;<br/>
<a NAME="E6:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</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="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E7:27"/><span class="lab"><font color="Green" title="E22">A7</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="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E23">A8</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E2:27_1"/><span class="lab"><font color="Green" title="E25">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="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E3:27_1"/><span class="lab"><font color="Green" title="E26">A11</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="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">a</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="Olive" title="b1">x</font>,<font color="Maroon" title="c5">c</font> )</span><br/><span class="kw">consider </span><font color="Maroon" title="c6">e1</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="E5:27_1"/><span class="lab"><font color="Green" title="E27">A12</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E6:27_1"/><span class="lab"><font color="Green" title="E28">A13</font></span>: 
<font color="Maroon" title="c2">p</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">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="pasch.html#T19" target="_self" title="PASCH:th.19">Th26</a></span>;<br/><a NAME="E7:27_1"/><span class="lab"><font color="Green" title="E29">A14</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="c5">c</font>,<font color="Maroon" title="c3">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:27_1_1"/><span class="lab"><font color="Green" title="E30">A15</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="c2">p</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="E2:27_1_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="c3">a</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/>

<span class="kw">hence </span><a NAME="E3:27_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E1:27_1_1"><span class="lab"><font color="Green" title="E30">A15</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="E8:27_1"/><span class="lab"><font color="Green" title="E30">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="c6">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">e1</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="E2:27_1_2"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_2"/><span class="kw">then </span>
(  <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="c5">c</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</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#T7" title="DIRAF:th.7">DIRAF:7</a></span>;<br/>
<a NAME="E4:27_1_2"/><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="c5">c</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</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#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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><span class="kw">consider </span><font color="Maroon" title="c7">e4</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="E10:27_1"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">e4</font>
 <span class="kw">and </span><br/><a NAME="E11:27_1"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<font color="Maroon" title="c6">e1</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="c7">e4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c8">e2</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="E13:27_1"/><span class="lab"><font color="Green" title="E33">A19</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">and </span><br/><a NAME="E14:27_1"/><span class="lab"><font color="Green" title="E34">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="c2">p</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c9">e3</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="E16:27_1"/><span class="lab"><font color="Green" title="E35">A21</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="c5">c</font>,<font color="Maroon" title="c9">e3</font>
 <span class="kw">and </span><br/><a NAME="E17:27_1"/><span class="lab"><font color="Green" title="E36">A22</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E18:27_1"/><span class="lab"><font color="Green" title="E37">A23</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_3"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<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="E2:27_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A24</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</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="E3:27_1_3"/><span class="lab"><font color="Green" title="E39">A25</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c4">b</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="E4:27_1_3"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">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="#E4:27"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:27_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E2:27_1_3"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E3:27_1_3"><span class="lab"><font color="Green" title="E39">A25</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="E19:27_1"/><span class="lab"><font color="Green" title="E38">A26</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="c8">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_4"/><span class="lab"><font color="Green" title="E39">A27</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">e2</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="E2:27_1_4"/>
<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="c5">c</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_4"/><span class="kw">then </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="c5">c</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E14:27_1"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E1:27_1_4"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_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="c4">b</font>,<font color="Maroon" title="c5">c</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="E5:27_1_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="c5">c</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</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="E6:27_1_4"/><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="c5">c</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</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="E7:27_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:27_1"><span class="lab"><font color="Green" title="E37">A23</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="E20:27_1"/><span class="lab"><font color="Green" title="E39">A28</font></span>: 
<font color="Maroon" title="c8">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">e3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_5"/>
<font color="Maroon" title="c8">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">e3</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="E2:27_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</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">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</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="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E19:27_1"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</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="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/>
<a NAME="E5:27_1_5"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">c</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#T7" title="DIRAF:th.7">DIRAF:7</a></span>;<br/>
<a NAME="E6:27_1_5"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">c</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="E7:27_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E21:27_1"/><span class="lab"><font color="Green" title="E40">A29</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">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_6"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">e1</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="E2:27_1_6"/><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="c5">c</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:27_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:27_1"><span class="lab"><font color="Green" title="E37">A23</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="E22:27_1"/><span class="lab"><font color="Green" title="E41">A30</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="c7">e4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_7"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e4</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="E2:27_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</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">by</span> <span class="lab"><a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</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">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E21:27_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_7"/><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="c3">a</font>,<font color="Maroon" title="c5">c</font> or  <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="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="E5:27_1_7"/><span class="kw">then </span>
(  <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="c5">c</font> or  <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">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="E6:27_1_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E23:27_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">e4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E24:27_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</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="E25:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A31</font></span>: 
<font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</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="E26:27_1"/>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E17:27_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E27:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A32</font></span>: 
<font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:27_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="txt" href="#E25:27_1"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E28:27_1"/><span class="lab"><font color="Green" title="E44">A33</font></span>: 
<font color="Maroon" title="c8">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_8"/>
<font color="Maroon" title="c8">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e4</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="E2:27_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E19:27_1"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</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="E5:27_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</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="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E21:27_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E6:27_1_8"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c5">c</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="E7:27_1_8"/><span class="kw">then </span>
(  <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="c5">c</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</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#T7" title="DIRAF:th.7">DIRAF:7</a></span>;<br/>
<a NAME="E8:27_1_8"/><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="c5">c</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</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#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:27_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E29:27_1"/><span class="lab"><font color="Green" title="E45">A34</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="c9">e3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_9"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">e3</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="E2:27_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</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="#E17:27_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</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="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E19:27_1"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_9"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c2">p</font> or  <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="c5">c</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="E5:27_1_9"/><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="c5">c</font>,<font color="Maroon" title="c2">p</font> or  <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="c5">c</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="E6:27_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E30:27_1"/><span class="lab"><font color="Green" title="E46">A35</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="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E31:27_1"/><span class="lab"><font color="Green" title="E47">A36</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="c9">e3</font>,<font color="Maroon" title="c8">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_10"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:27_1_10"/>
<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="c5">c</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E2:27_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A37</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="c4">b</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="E3:27_1_10"/>
<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="c9">e3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E4:27_1_10"/><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="c2">p</font>,<font color="Maroon" title="c9">e3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E2:27_1_10"><span class="lab"><font color="Green" title="E48">A37</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E5:27_1_10"/><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">b</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c4">b</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="E6:27_1_10"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c4">b</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="E7:27_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A38</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</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="E8:27_1_10"/><span class="lab"><font color="Green" title="E50">A39</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c2">p</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="E9:27_1_10"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E10:27_1_10"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c5">c</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="E11:27_1_10"/><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="c5">c</font>,<font color="Maroon" title="c8">e2</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c5">c</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="E12:27_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A40</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</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="E13:27_1_10"/>
<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="c9">e3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/>
<a NAME="E14:27_1_10"/><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="c5">c</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</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="E15:27_1_10"/><span class="kw">then </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="c9">e3</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</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="E16:27_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A41</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</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/>
<span class="kw">assume </span><a NAME="E17:27_1_10"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</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="E18:27_1_10"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:27_1"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="txt" href="#E16:27_1_10"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="txt" href="#E12:27_1_10"><span class="lab"><font color="Green" title="E51">A40</font></span></a>, <a class="ref" href="diraf.html#T35" title="DIRAF:th.35">DIRAF:35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:27_1_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E30:27_1"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="txt" href="#E7:27_1_10"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E8:27_1_10"><span class="lab"><font color="Green" title="E50">A39</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="E32:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A42</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</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/><span class="kw">consider </span><font color="Maroon" title="c10">e5</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="E34:27_1"/><span class="lab"><font color="Green" title="E49">A43</font></span>: 
<font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">and </span><br/><a NAME="E35:27_1"/><span class="lab"><font color="Green" title="E50">A44</font></span>: 
<font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">and </span><br/><a NAME="E36:27_1"/><span class="lab"><font color="Green" title="E51">A45</font></span>: 
<font color="Maroon" title="c8">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">e5</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="E37:27_1"/><span class="lab"><font color="Green" title="E52">A46</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_11"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:27_1_11"/>
<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="c5">c</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E2:27_1_11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A47</font></span>: 
<font color="Maroon" title="c5">c</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">by</span> <span class="lab"><a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:27_1_11"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">e1</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="E4:27_1_11"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</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">by</span> <span class="lab"><a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E2:27_1_11"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E5:27_1_11"/><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="c3">a</font>,<font color="Maroon" title="c5">c</font> or  <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="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="E6:27_1_11"/><span class="kw">then </span>
(  <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="c5">c</font> or  <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">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="E7:27_1_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E38:27_1"/><span class="lab"><font color="Green" title="E53">A48</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="c7">e4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_12"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_12"/><span class="lab"><font color="Green" title="E54">A49</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e4</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="E2:27_1_12"/>
<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="c5">c</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<a NAME="E3:27_1_12"/><span class="kw">then </span>
<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E11:27_1"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E1:27_1_12"><span class="lab"><font color="Green" title="E54">A49</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_12"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</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="E5:27_1_12"/><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="c6">e1</font>,<font color="Maroon" title="c5">c</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</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="E6:27_1_12"/><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="c6">e1</font>,<font color="Maroon" title="c5">c</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</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="E7:27_1_12"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A50</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</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="E8:27_1_12"/><span class="lab"><font color="Green" title="E56">A51</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c4">b</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="E9:27_1_12"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:27_1_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:27_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E37:27_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="txt" href="#E7:27_1_12"><span class="lab"><font color="Green" title="E55">A50</font></span></a>, <a class="txt" href="#E8:27_1_12"><span class="lab"><font color="Green" title="E56">A51</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="E39:27_1"/><span class="lab"><font color="Green" title="E54">A52</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="c10">e5</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_13"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_13"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e5</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="E2:27_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">e4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:27_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E38:27_1"><span class="lab"><font color="Green" title="E53">A48</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</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="E5:27_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E19:27_1"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E6:27_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</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="E7:27_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</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="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E21:27_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E8:27_1_13"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c5">c</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="E9:27_1_13"/><span class="kw">then </span>
(  <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="c5">c</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</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#T7" title="DIRAF:th.7">DIRAF:7</a></span>;<br/>
<a NAME="E10:27_1_13"/><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="c5">c</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</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#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:27_1_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E40:27_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27_1"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a></span>;<br/><a NAME="E41:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A53</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">e1</font>,<font color="Maroon" title="c4">b</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="E42:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">e1</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="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E43:27_1"/><span class="kw">then </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="c6">e1</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27_1"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E41:27_1"><span class="lab"><font color="Green" title="E55">A53</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E44:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">e1</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="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E14:27_1"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E45:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A54</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">e4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:27_1"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E37:27_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E46:27_1"/>
 <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="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E47:27_1"/><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="c7">e4</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:27_1"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E27:27_1"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E22:27_1"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E45:27_1"><span class="lab"><font color="Green" title="E56">A54</font></span></a>, <a class="ref" href="pasch.html#T16" target="_self" title="PASCH:th.16">Th23</a></span>;<br/><a NAME="E48:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A55</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">e4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c8">e2</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="E49:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">e4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">e2</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="E50:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A56</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:27_1"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E48:27_1"><span class="lab"><font color="Green" title="E57">A55</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E51:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A57</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:27_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E28:27_1"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E52:27_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_14"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_14"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">e2</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="E2:27_1_14"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</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="#E13:27_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:27_1_14"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27_1"><span class="lab"><font color="Green" title="E29">A14</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="E53:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A58</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="c7">e4</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:27_1"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E50:27_1"><span class="lab"><font color="Green" title="E58">A56</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E54:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A59</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="c5">c</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:27_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E28:27_1"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E55:27_1"/><span class="lab"><font color="Green" title="E62">A60</font></span>: 
<font color="Maroon" title="c10">e5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">e3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_15"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:27_1_15"/>
<font color="Maroon" title="c10">e5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">e3</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="E2:27_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c9">e3</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="#E54:27_1"><span class="lab"><font color="Green" title="E61">A59</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/>
<a NAME="E3:27_1_15"/><span class="kw">then </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="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E29:27_1"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E4:27_1_15"/><span class="kw">then </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="c4">b</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="E5:27_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</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="#E6:27"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/>
<a NAME="E6:27_1_15"/><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="c5">c</font>,<font color="Maroon" title="c3">a</font> or  <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="c5">c</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="E7:27_1_15"/><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="c5">c</font>,<font color="Maroon" title="c3">a</font> or  <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="c5">c</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="E8:27_1_15"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:27_1"><span class="lab"><font color="Green" title="E37">A23</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="E56:27_1"/>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">e4</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E57:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:27_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E38:27_1"><span class="lab"><font color="Green" title="E53">A48</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E58:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:27_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E21:27_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E59:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E17:27_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E60:27_1"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</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="E61:27_1"/><span class="kw">then </span>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</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="E62:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A61</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</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="E63:27_1"/>
 <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="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E64:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A62</font></span>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c9">e3</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#T9" title="DIRAF:th.9">DIRAF:9</a></span>;<br/><a NAME="E65:27_1"/>
<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</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="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">x</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="E67:27_1"/><span class="lab"><font color="Green" title="E65">A63</font></span>: 
<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c11">x</font>
 <span class="kw">and </span><br/><a NAME="E68:27_1"/><span class="lab"><font color="Green" title="E66">A64</font></span>: 
<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:27_1"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E69:27_1"/><span class="lab"><font color="Green" title="E67">A65</font></span>: 
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">e5</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E67:27_1"><span class="lab"><font color="Green" title="E65">A63</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E70:27_1"/>
 <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="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:27_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E71:27_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c9">e3</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#T9" title="DIRAF:th.9">DIRAF:9</a></span>;<br/><a NAME="E72:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</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="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E73:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c2">p</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="E74:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">c</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="E75:27_1"/><span class="kw">then </span>
 not  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:27_1"><span class="lab"><font color="Green" title="E62">A60</font></span></a>, <a class="txt" href="#E51:27_1"><span class="lab"><font color="Green" title="E59">A57</font></span></a>, <a class="txt" href="#E32:27_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="ref" href="pasch.html#T17" target="_self" title="PASCH:th.17">Th24</a></span>;<br/><a NAME="E76:27_1"/><span class="kw">then </span>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:27_1"><span class="lab"><font color="Green" title="E63">A61</font></span></a>, <a class="ref" href="diraf.html#T29" title="DIRAF:th.29">DIRAF:29</a></span>;<br/><a NAME="E77:27_1"/><span class="kw">then </span>
( <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c8">e2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T9" title="DIRAF:th.9">DIRAF:9</a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E78:27_1"/><span class="kw">then </span>
( <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font> or <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c8">e2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></span>;<br/><a NAME="E79:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A66</font></span>: 
<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E80:27_1"/>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">e5</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:27_1"><span class="lab"><font color="Green" title="E59">A57</font></span></a>, <a class="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><a NAME="E81:27_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c8">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:27_1"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E32:27_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E79:27_1"><span class="lab"><font color="Green" title="E68">A66</font></span></a>, <a class="txt" href="#E64:27_1"><span class="lab"><font color="Green" title="E64">A62</font></span></a>, <a class="ref" href="pasch.html#T15" target="_self" title="PASCH:th.15">Th22</a></span>;<br/><a NAME="E82:27_1"/><span class="kw">then </span>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</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="E83:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A67</font></span>: 
<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</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="E84:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c10">e5</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</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="E85:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:27_1"><span class="lab"><font color="Green" title="E51">A45</font></span></a>, <a class="txt" href="#E83:27_1"><span class="lab"><font color="Green" title="E69">A67</font></span></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></span>;<br/><a NAME="E86:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">e5</font>,<font color="Maroon" title="c9">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:27_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E20:27_1"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E87:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E68:27_1"><span class="lab"><font color="Green" title="E66">A64</font></span></a>, <a class="txt" href="#E55:27_1"><span class="lab"><font color="Green" title="E62">A60</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E88:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A68</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c11">x</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="E89:27_1"/>
<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">c</font>,<font color="Maroon" title="c10">e5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:27_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E28:27_1"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="txt" href="#E53:27_1"><span class="lab"><font color="Green" title="E60">A58</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E90:27_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A69</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="c11">x</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:27_1"><span class="lab"><font color="Green" title="E54">A52</font></span></a>, <a class="txt" href="#E69:27_1"><span class="lab"><font color="Green" title="E67">A65</font></span></a>, <a class="ref" href="diraf.html#T3" title="DIRAF:th.3">DIRAF:3</a></span>;<br/><a NAME="E91:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c11">x</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="ref" href="diraf.html#T2" title="DIRAF:th.2">DIRAF:2</a></span>;<br/><span class="kw">hence </span><a NAME="E92:27_1"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">a</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="Olive" title="b1">x</font>,<font color="Maroon" title="c5">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E90:27_1"><span class="lab"><font color="Green" title="E71">A69</font></span></a>, <a class="txt" href="#E88:27_1"><span class="lab"><font color="Green" title="E70">A68</font></span></a>, <a class="ref" href="pasch.html#T15" target="_self" title="PASCH:th.15">Th22</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="E9:27"/><span class="lab"><font color="Green" title="E24">A70</font></span>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> implies ( <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="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</a>, <a class="ref" href="diraf.html#T10" title="DIRAF:th.10">DIRAF:10</a></span>;<br/>
<a NAME="E10:27"/><span class="lab"><font color="Green" title="E25">A71</font></span>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> implies ( <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">c</font>,<font color="Maroon" title="c5">c</font> &amp;  <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="c3">a</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T4" title="DIRAF:th.4">DIRAF:4</a>, <a class="ref" href="diraf.html#T10" title="DIRAF:th.10">DIRAF:10</a></span>;<br/>
<a NAME="E11:27"/>
( <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> implies ( <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="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T1" title="DIRAF:th.1">DIRAF:1</a>, <a class="ref" href="diraf.html#T10" title="DIRAF:th.10">DIRAF:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:27"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> st <br/>(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c3">a</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="Olive" title="b1">x</font>,<font color="Maroon" title="c5">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E24">A70</font></span></a>, <a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E25">A71</font></span></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>
