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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">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">a'</font>, <font color="Olive" title="b5">b'</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; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b4">a'</font> &amp; <font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">b'</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">a'</font>,<font color="Olive" title="b5">b'</font> holds <br/><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b'</font>,<font color="Olive" title="b4">a'</font></span><br/><b>let </b><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">a'</font>, <font color="Maroon" title="c6">b'</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"> ( 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; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a'</font> &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b'</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">a'</font>,<font color="Maroon" title="c6">b'</font> implies <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c5">a'</font> )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E8">A1</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="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a'</font>
 <b>and </b><br/><a NAME="E3:18"/><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b'</font>
 <b>and </b><br/><a NAME="E4:18"/><i><font color="Green" title="E11">A4</font></i>: 
<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">a'</font>,<font color="Maroon" title="c6">b'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c5">a'</font></span><br/>

<a NAME="E5:18"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="#E1:18"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">q</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="E7:18"/><i><font color="Green" title="E12">A5</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">q</font>
 <b>and </b><br/><a NAME="E8:18"/><i><font color="Green" title="E13">A6</font></i>: 
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c7">q</font>
 <b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E9:18"/><i><font color="Green" title="E14">A7</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="c4">b</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="#E1:18"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E10:18"/>
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a'</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b'</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">q</font> )
 
<b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="#E3:18"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="#E7:18"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<a NAME="E11:18"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">a'</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">b'</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c7">q</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E12:18"/><b>then </b><i><font color="Green" title="E15">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="c3">a</font>,<font color="Maroon" title="c5">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="c4">b</font>,<font color="Maroon" title="c6">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="c7">q</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E13:18"/>
( <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font> &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c7">q</font> )
 
<b>by </b><i><a class="txt" href="#E4:18"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="#E8:18"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a>, <a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></i>;<br/>
<a NAME="E14:18"/><b>then </b>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>
 
<b>by </b><i><a class="txt" href="#E8:18"><i><font color="Green" title="E13">A6</font></i></a>, <a class="txt" href="#E9:18"><i><font color="Green" title="E14">A7</font></i></a>, <a class="txt" href="#E12:18"><i><font color="Green" title="E15">A8</font></i></a>, <a class="ref" href="pasch.html#T11" target="_self" title="PASCH:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E15:18"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c5">a'</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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