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











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:32"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">and </span><br/><a NAME="E2:32"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 <span class="kw">and </span><br/><a NAME="E3:32"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">and </span><br/><a NAME="E4:32"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</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="c6">p</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><br/>

<a NAME="E5:32"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">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/>
<span class="kw">assume </span><a NAME="E6:32"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="E7:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A6</font></span>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E3:32"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:32"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E5:32"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="diraf.html#T32" title="DIRAF:th.32">DIRAF:32</a></span>;<br/>
<a NAME="E8:32"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="diraf.html#T22" title="DIRAF:th.22">DIRAF:22</a></span>;<br/>
<a NAME="E9:32"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:32"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E7:32"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E8:32"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="diraf.html#T33" title="DIRAF:th.33">DIRAF:33</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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