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<span class="kw">let </span><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">d1</font>, <font color="Olive" title="b6">d2</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#R3" title="DIRAF:pred.3">LIN</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> &amp;  <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="b5">d1</font> &amp;  <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="b6">d2</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">d1</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b4">c</font>,<font color="Olive" title="b6">d2</font> holds <br/><font color="Olive" title="b5">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">d2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d1</font>, <font color="Maroon" title="c7">d2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 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#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="c5">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="c3">a</font>,<font color="Maroon" title="c6">d1</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">a</font>,<font color="Maroon" title="c7">d2</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">d2</font> implies <font color="Maroon" title="c6">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d2</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E4">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="E2:17"/><span class="lab"><font color="Green" title="E5">A2</font></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="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E3:17"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d1</font>
 <span class="kw">and </span><br/><a NAME="E4:17"/><span class="lab"><font color="Green" title="E7">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="c3">a</font>,<font color="Maroon" title="c7">d2</font>
 <span class="kw">and </span><br/><a NAME="E5:17"/><span class="lab"><font color="Green" title="E8">A5</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d1</font>
 <span class="kw">and </span><br/><a NAME="E6:17"/><span class="lab"><font color="Green" title="E9">A6</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d2</font></span><br/>

<a NAME="E7:17"/><span class="lab"><font color="Green" title="E10">A7</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="#E1:17"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/>
<a NAME="E8:17"/><span class="lab"><font color="Green" title="E11">A8</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="#E1:17"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E12">A9</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:17_1"/>
 <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="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E2:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A10</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><a NAME="E3:17_1"/><span class="lab"><font color="Green" title="E14">A11</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c6">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E4:17_1"/><span class="lab"><font color="Green" title="E15">A12</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E5:17_1"/><span class="lab"><font color="Green" title="E16">A13</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E6:17_1"/><span class="lab"><font color="Green" title="E17">A14</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E7:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A15</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><a NAME="E8:17_1"/>
<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d1</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></span>;<br/><a NAME="E9:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A16</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></span>;<br/><a NAME="E10:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A17</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><span class="kw">assume </span><a NAME="E11:17_1"/><span class="lab"><font color="Green" title="E21">A18</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c6">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d2</font></span><br/><span class="kw">assume </span><a NAME="E12:17_1"/><span class="lab"><font color="Green" title="E22">A19</font></span>: 
<font color="Maroon" title="c6">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E13:17_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E6:17_1"><span class="lab"><font color="Green" title="E17">A14</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><a NAME="E14:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A20</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E10:17_1"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="txt" href="#E3:17_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><a NAME="E15:17_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:17_1"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/><a NAME="E16:17_1"/><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="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E7:17_1"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E5:17_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><a NAME="E17:17_1"/><span class="kw">then </span>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17_1"><span class="lab"><font color="Green" title="E21">A18</font></span></a>, <a class="txt" href="#E14:17_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E4:17_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>;<br/><span class="kw">hence </span><a NAME="E18:17_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E12:17_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E7:17_1"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E2:17_1"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E10:17"/><span class="lab"><font color="Green" title="E13">A21</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/>
<a NAME="E11:17"/><span class="lab"><font color="Green" title="E14">A22</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:17_2"/><span class="lab"><font color="Green" title="E15">A23</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">d2</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><span class="kw">assume </span><a NAME="E2:17_2"/><span class="lab"><font color="Green" title="E16">A24</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d2</font></span><br/><a NAME="E3:17_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A25</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">d2</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:17_2_1"/><span class="lab"><font color="Green" title="E19">A27</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">d2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:17_2_1"/><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="c7">d2</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:17"><span class="lab"><font color="Green" title="E13">A21</font></span></a>, <a class="txt" href="#E3:17_2"><span class="lab"><font color="Green" title="E17">A25</font></span></a>, <a class="ref" href="diraf.html#T39" title="DIRAF:th.39">DIRAF:39</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E10:17"><span class="lab"><font color="Green" title="E13">A21</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E15">A23</font></span></a>, <a class="txt" href="#E1:17_2_1"><span class="lab"><font color="Green" title="E19">A27</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E5:17_2"/><span class="lab"><font color="Green" title="E19">A28</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d1</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></span>;<br/><a NAME="E6:17_2"/><span class="lab"><font color="Green" title="E20">A29</font></span>: 
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">d1</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E2:17_2"><span class="lab"><font color="Green" title="E16">A24</font></span></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:17_2_2"/><span class="lab"><font color="Green" title="E21">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="c6">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:17_2_2"/><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="c6">d1</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E14">A22</font></span></a>, <a class="txt" href="#E6:17_2"><span class="lab"><font color="Green" title="E20">A29</font></span></a>, <a class="ref" href="diraf.html#T39" title="DIRAF:th.39">DIRAF:39</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E14">A22</font></span></a>, <a class="txt" href="#E5:17_2"><span class="lab"><font color="Green" title="E19">A28</font></span></a>, <a class="txt" href="#E1:17_2_2"><span class="lab"><font color="Green" title="E21">A30</font></span></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E8:17_2"/>
<font color="Maroon" title="c6">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17_2"><span class="lab"><font color="Green" title="E18">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:17"/>
<font color="Maroon" title="c6">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E12">A9</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
