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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">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="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#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="E1:10"/><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="E2:10"/><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="E3:10"/><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="E4:10"/><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="E5:10"/><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="E6:10"/><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="firebrick">::  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="E7:10"/><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="#E1:10"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<a NAME="E8:10"/><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="#E1:10"><span class="lab"><font color="Green" title="E4">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="E12">A9</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:10_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#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><a NAME="E2:10_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="#E3:10"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><a NAME="E3:10_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#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><a NAME="E4:10_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="#E2:10"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/><a NAME="E5:10_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#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><a NAME="E6:10_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#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><a NAME="E7:10_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="#E3:10"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><a NAME="E8:10_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="#E5:10"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="ref" href="diraf.html#T23" title="DIRAF:th.23">DIRAF:23</a></span>;<br/><a NAME="E9:10_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="E10:10_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#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/><span class="kw">assume </span><a NAME="E11:10_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="firebrick">::  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="E12:10_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="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E13:10_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="#E3:10"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E6:10_1"><span class="lab"><font color="Green" title="E17">A14</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><a NAME="E14:10_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="#E12:10_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E10:10_1"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="txt" href="#E3:10_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><a NAME="E15:10_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="#E9:10_1"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/><a NAME="E16:10_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="#E12:10_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E7:10_1"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E5:10_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><a NAME="E17:10_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="#E11:10_1"><span class="lab"><font color="Green" title="E21">A18</font></span></a>, <a class="txt" href="#E14:10_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E4:10_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/><span class="kw">hence </span><a NAME="E18:10_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E12:10_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E7:10_1"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E2:10_1"><span class="lab"><font color="Green" title="E13">A10</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="E10:10"/><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="#E4:10"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<a NAME="E11:10"/><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="#E3:10"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="ref" href="diraf.html#T30" title="DIRAF:th.30">DIRAF:30</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:10_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#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><span class="kw">assume </span><a NAME="E2:10_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="firebrick">::  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="E3:10_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="#E6:10"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="diraf.html#T22" title="DIRAF:th.22">DIRAF:22</a></span>;<br/><div><span class="lab"><font color="Green" title="E18">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:10_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="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:10_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="#E10:10"><span class="lab"><font color="Green" title="E13">A21</font></span></a>, <a class="txt" href="#E3:10_2"><span class="lab"><font color="Green" title="E17">A25</font></span></a>, <a class="ref" href="diraf.html#T33" title="DIRAF:th.33">DIRAF:33</a></span>;<br/><span class="kw">hence </span><a NAME="E3:10_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A21</font></span></a>, <a class="txt" href="#E1:10_2"><span class="lab"><font color="Green" title="E15">A23</font></span></a>, <a class="txt" href="#E1:10_2_1"><span class="lab"><font color="Green" title="E19">A27</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="E5:10_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#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/><a NAME="E6:10_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="#E5:10"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E2:10_2"><span class="lab"><font color="Green" title="E16">A24</font></span></a>, <a class="ref" href="diraf.html#T22" title="DIRAF:th.22">DIRAF:22</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:10_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="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:10_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="#E11:10"><span class="lab"><font color="Green" title="E14">A22</font></span></a>, <a class="txt" href="#E6:10_2"><span class="lab"><font color="Green" title="E20">A29</font></span></a>, <a class="ref" href="diraf.html#T33" title="DIRAF:th.33">DIRAF:33</a></span>;<br/><span class="kw">hence </span><a NAME="E3:10_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E14">A22</font></span></a>, <a class="txt" href="#E5:10_2"><span class="lab"><font color="Green" title="E19">A28</font></span></a>, <a class="txt" href="#E1:10_2_2"><span class="lab"><font color="Green" title="E21">A30</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><span class="kw">hence </span><a NAME="E8:10_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="#E4:10_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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:10"/>
<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="#E9:10"><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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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