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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">c</font>,<font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">a</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">a</font> &amp; not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">a</font>,<font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">c</font> holds <br/> <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">a</font></span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">a</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font> &amp; not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> implies  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font> )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:21"/><i><font color="Green" title="E10">A1</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font>
 <b>and </b><br/><a NAME="E3:21"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>
 <b>and </b><br/><a NAME="E4:21"/><i><font color="Green" title="E13">A4</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font>
 <b>and </b><br/><a NAME="E5:21"/><i><font color="Green" title="E14">A5</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font></span><br/>

<a NAME="E6:21"/><i><font color="Green" title="E15">A6</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1"/><i><font color="Green" title="E16">A7</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font></span><br/><a NAME="E2:21_1"/><b>then </b><i><font color="Green" title="E17">A8</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><div><i><font color="Green" title="E18">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_1"/><i><font color="Green" title="E19">A10</font></i>: 
( <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font></span><br/><a NAME="E2:21_1_1"/><i><font color="Green" title="E20">A11</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><b>assume </b><a NAME="E3:21_1_1"/>
not  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E4:21_1_1"/><b>then </b>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="#E3:21"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>;<br/><a NAME="E5:21_1_1"/><b>then </b>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E7:21_1_1"/><i><font color="Green" title="E21">A12</font></i>: 
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">e1</font>
 <b>and </b><br/><a NAME="E8:21_1_1"/><i><font color="Green" title="E22">A13</font></i>: 
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font>
 <b>by </b><i><a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E9:21_1_1"/><i><font color="Green" title="E23">A14</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">e1</font>
 <b>by </b><i><a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E10:21_1_1"/><b>then </b><i><font color="Green" title="E24">A15</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">e1</font>
 <b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><b>consider </b><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><b> such that </b><br/><a NAME="E12:21_1_1"/><i><font color="Green" title="E25">A16</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">e2</font>
 <b>and </b><br/><a NAME="E13:21_1_1"/><i><font color="Green" title="E26">A17</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E6:21"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E14:21_1_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="txt" href="#E12:21_1_1"><i><font color="Green" title="E25">A16</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E15:21_1_1"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><a NAME="E16:21_1_1"/><b>then </b><i><font color="Green" title="E27">A18</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><a NAME="E17:21_1_1"/><i><font color="Green" title="E28">A19</font></i>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="#E12:21_1_1"><i><font color="Green" title="E25">A16</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E18:21_1_1"/><i><font color="Green" title="E29">A20</font></i>: 
<font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_1"/>
<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:21_1_1_1"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>
 
<b>by </b><i><a class="txt" href="#E9:21_1_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E3:21_1_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">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">d</font>,<font color="Maroon" title="c6">a</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font> ) )
 
<b>by </b><i><a class="txt" href="#E3:21"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E4:21_1_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">c</font> &amp; (  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font> ) )
 
<b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E5:21_1_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">c</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c2">p</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E6:21_1_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c2">p</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c6">a</font> )
 
<b>by </b><i><a class="txt" href="#E5:21"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E6:21"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a>, <a class="ref" href="diraf.html#T41" title="DIRAF:th.41">DIRAF:41</a></i>;<br/>
<b>hence </b><a NAME="E7:21_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E19:21_1_1"/><i><font color="Green" title="E30">A21</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_2"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:21_1_1_2"/><b>then </b>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E6:21"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="diraf.html#T12" title="DIRAF:th.12">DIRAF:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>consider </b><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><b> such that </b><br/><a NAME="E21:21_1_1"/><i><font color="Green" title="E31">A22</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">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>
 <b>and </b><br/><a NAME="E22:21_1_1"/><i><font color="Green" title="E32">A23</font></i>: 
( <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c9">e3</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">e3</font> )
 <b>by </b><i><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E23:21_1_1"/><i><font color="Green" title="E33">A24</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c3">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:21_1_1_3"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">e2</font>
 
<b>by </b><i><a class="txt" href="#E12:21_1_1"><i><font color="Green" title="E25">A16</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E2:21_1_1_3"/><b>then </b>
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c8">e2</font>
 
<b>by </b><i><a class="txt" href="#E2:21"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="#E2:21_1_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/>
<a NAME="E3:21_1_1_3"/><b>then </b>
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c9">e3</font>
 
<b>by </b><i><a class="txt" href="#E17:21_1_1"><i><font color="Green" title="E28">A19</font></i></a>, <a class="txt" href="#E22:21_1_1"><i><font color="Green" title="E32">A23</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/>
<a NAME="E4:21_1_1_3"/><b>then </b>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>;<br/>
<a NAME="E5:21_1_1_3"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<b>hence </b><a NAME="E6:21_1_1_3"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E24:21_1_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></i>;<br/><a NAME="E25:21_1_1"/><b>then </b><i><font color="Green" title="E34">A25</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E26:21_1_1"/><b>then </b>
<font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="#E13:21_1_1"><i><font color="Green" title="E26">A17</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E27:21_1_1"/><b>then </b><i><font color="Green" title="E35">A26</font></i>: 
<font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font>
 <b>by </b><i><a class="txt" href="#E5:21"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E8:21_1_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/><a NAME="E28:21_1_1"/><b>then </b>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/><a NAME="E29:21_1_1"/><b>then </b><i><font color="Green" title="E36">A27</font></i>: 
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E30:21_1_1"/><b>then </b>
( <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font> )
 <b>by </b><i><a class="txt" href="#E8:21_1_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/><a NAME="E31:21_1_1"/><b>then </b>
( <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c3">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">c</font> )
 <b>by </b><i><a class="txt" href="#E18:21_1_1"><i><font color="Green" title="E29">A20</font></i></a>, <a class="txt" href="#E25:21_1_1"><i><font color="Green" title="E34">A25</font></i></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/><a NAME="E32:21_1_1"/><b>then </b>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="#E5:21"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/><a NAME="E33:21_1_1"/><b>then </b><i><font color="Green" title="E37">A28</font></i>: 
<font color="Maroon" title="c5">d</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="c9">e3</font>
 <b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="#E21:21_1_1"><i><font color="Green" title="E31">A22</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/><a NAME="E34:21_1_1"/><b>then </b>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>
 <b>by </b><i><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E35:21_1_1"/><b>then </b><i><font color="Green" title="E38">A29</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font>,<font color="Maroon" title="c9">e3</font>
 <b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><a NAME="E36:21_1_1"/><i><font color="Green" title="E39">A30</font></i>: 
<font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="txt" href="#E18:21_1_1"><i><font color="Green" title="E29">A20</font></i></a>, <a class="txt" href="#E27:21_1_1"><i><font color="Green" title="E35">A26</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E37:21_1_1"/><b>then </b><i><font color="Green" title="E40">A31</font></i>: 
<font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">e3</font>
 <b>by </b><i><a class="txt" href="#E33:21_1_1"><i><font color="Green" title="E37">A28</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E38:21_1_1"/><i><font color="Green" title="E41">A32</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_4"/><i><font color="Green" title="E42">A33</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:21_1_1_4"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">d</font>
 
<b>by </b><i><a class="txt" href="#E1:21_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<a NAME="E3:21_1_1_4"/><b>then </b>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E4:21_1_1_4"/><b>then </b>
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="#E8:21_1_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="txt" href="#E1:21_1_1_4"><i><font color="Green" title="E42">A33</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/>
<a NAME="E5:21_1_1_4"/><b>then </b>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E6:21_1_1_4"/><b>then </b>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">c</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>;<br/>
<a NAME="E7:21_1_1_4"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">c</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E8:21_1_1_4"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">p</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/>
<b>hence </b><a NAME="E9:21_1_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E5:21"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="#E6:21"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E39:21_1_1"/><i><font color="Green" title="E42">A34</font></i>: 
<font color="Maroon" title="c6">a</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="21_1_1_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1_1_5"/><i><font color="Green" title="E43">A35</font></i>: 
<font color="Maroon" title="c6">a</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:21_1_1_5"/>
<font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="#E7:21_1_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E3:21_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="#E13:21_1_1"><i><font color="Green" title="E26">A17</font></i></a>, <a class="txt" href="#E38:21_1_1"><i><font color="Green" title="E41">A32</font></i></a>, <a class="txt" href="#E1:21_1_1_5"><i><font color="Green" title="E43">A35</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/>
<a NAME="E4:21_1_1_5"/><b>then </b>
<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E5:21_1_1_5"/><b>then </b>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>;<br/>
<a NAME="E6:21_1_1_5"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E7:21_1_1_5"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="txt" href="#E6:21"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/>
<b>hence </b><a NAME="E8:21_1_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E40:21_1_1"/>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c8">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>
 <b>by </b><i><a class="txt" href="#E33:21_1_1"><i><font color="Green" title="E37">A28</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E41:21_1_1"/><b>then </b>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>
 <b>by </b><i><a class="txt" href="#E29:21_1_1"><i><font color="Green" title="E36">A27</font></i></a>, <a class="txt" href="#E36:21_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/><a NAME="E42:21_1_1"/><b>then </b>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c7">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>;<br/><a NAME="E43:21_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c9">e3</font> or  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c7">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><a NAME="E44:21_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c7">e1</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c7">e1</font>,<font color="Maroon" title="c6">a</font> )
 <b>by </b><i><a class="txt" href="#E10:21_1_1"><i><font color="Green" title="E24">A15</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><a NAME="E45:21_1_1"/><b>then </b><i><font color="Green" title="E43">A36</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="txt" href="#E19:21_1_1"><i><font color="Green" title="E30">A21</font></i></a>, <a class="txt" href="#E23:21_1_1"><i><font color="Green" title="E33">A24</font></i></a>, <a class="ref" href="diraf.html#T41" title="DIRAF:th.41">DIRAF:41</a></i>;<br/><a NAME="E46:21_1_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c8">e2</font>
 <b>by </b><i><a class="txt" href="#E35:21_1_1"><i><font color="Green" title="E38">A29</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><a NAME="E47:21_1_1"/><b>then </b><i><font color="Green" title="E44">A37</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="#E16:21_1_1"><i><font color="Green" title="E27">A18</font></i></a>, <a class="txt" href="#E39:21_1_1"><i><font color="Green" title="E42">A34</font></i></a>, <a class="txt" href="#E45:21_1_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="ref" href="diraf.html#T41" title="DIRAF:th.41">DIRAF:41</a></i>;<br/><a NAME="E48:21_1_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="#E6:21"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><a NAME="E49:21_1_1"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c9">e3</font>,<font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="#E23:21_1_1"><i><font color="Green" title="E33">A24</font></i></a>, <a class="txt" href="#E47:21_1_1"><i><font color="Green" title="E44">A37</font></i></a>, <a class="ref" href="diraf.html#T41" title="DIRAF:th.41">DIRAF:41</a></i>;<br/><b>hence </b><a NAME="E50:21_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="#E37:21_1_1"><i><font color="Green" title="E40">A31</font></i></a>, <a class="txt" href="#E45:21_1_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="txt" href="#E47:21_1_1"><i><font color="Green" title="E44">A37</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:21_1_2"/>
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font></span><br/><a NAME="E2:21_1_2"/><b>then </b>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">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="c6">a</font>,<font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="txt" href="#E2:21"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>;<br/><a NAME="E3:21_1_2"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">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="c6">a</font>,<font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><a NAME="E4:21_1_2"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">b</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c2">p</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c6">a</font> )
 <b>by </b><i><a class="txt" href="#E2:21_1"><i><font color="Green" title="E17">A8</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><b>hence </b><a NAME="E5:21_1_2"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="#E4:21"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:21_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="txt" href="#E3:21_1"><i><font color="Green" title="E18">A9</font></i></a>, <a class="ref" href="diraf.html#T14" title="DIRAF:th.14">DIRAF:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:21"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="txt" href="#E3:21"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="diraf.html#T11" title="DIRAF:th.11">DIRAF:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
