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<b>let </b><font color="Maroon">SAS</font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">SAS</font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a> 
 ;<br/>

<b>let </b><font color="Maroon">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>, <font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>, <font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>, <font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>, <font color="Maroon">c'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:2"/><i><font color="Green">E16</font></i>: 
( not <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font> &amp; not <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c</font> )
 <b>and </b><br/><a NAME="E3:2"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c'</font> )
 <b>and </b><br/><a NAME="E4:2"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font> )
 ;<br/>

<a NAME="E5:2"/><i><font color="Green">E19</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">c'</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">A</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E7:2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>and </b><br/><a NAME="E8:2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>consider </b><font color="Maroon">P</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E10:2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">P</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>and </b><br/><a NAME="E11:2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">b'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>consider </b><font color="Maroon">C</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E13:2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">C</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>and </b><br/><a NAME="E14:2"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">c'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E15:2"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>
<a NAME="E16:2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">P</font>
 
<b>by </b><i>, <a class="ref" href="pardepap.html#T1" target="_self">Th1</a>, , , <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<a NAME="E17:2"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="pardepap.html#T1" target="_self">Th1</a>, , , <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<b>hence </b><a NAME="E18:2"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 <b>by </b><i>, , <a class="ref" href="pardepap.html#T1" target="_self">Th1</a>, , , , , , , <a class="txt" href="pardepap.html#E1:2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="aff_2.html#D4">AFF_2:def 4</a></i>;<br/>


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