<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/>

<b>assume </b><a NAME="E1:32"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR8" target="_self">satisfies_TDES_1</a> 
 ;<br/>

<b>thus </b><a NAME="E2:32"/>
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR9" target="_self">satisfies_TDES_2</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="aff_2.html#D9" target="_self">AFF_2:def 9</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>















<b>assume </b><a NAME="E1:32_1"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:32_1"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E3:32_1"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>
<a NAME="E4:32_1"/><i><font color="Green">E19</font></i>: 
not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T49">AFF_1:49</a></i>;<br/>
<a NAME="E5:32_1"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T49">AFF_1:49</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E6:32_1"/><i><font color="Green">E21</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E5:32_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E7:32_1"/><b>then </b><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E5:32_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E8:32_1"/><i><font color="Green">E23</font></i>: 
not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:32_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:32_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E4:32_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E7:32_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>
<a NAME="E3:32_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:32_1_1"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E4:32_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E2:32_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/>
<a NAME="E5:32_1_1"/><b>then </b>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E7:32_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/>
<b>hence </b><a NAME="E6:32_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E3:32_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="aff_2.html#E4:32_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E1:32_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_2.html#E3:32_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E9:32_1"/><i><font color="Green">E24</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E8:32_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E11:32_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/>
<a NAME="E12:32_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>13</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E11:32_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/>
<a NAME="E13:32_1"/>
not <font color="Maroon">c<sub>13</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:32_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E2:32_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E11:32_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<b>hence </b><a NAME="E3:32_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E8:32_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="aff_2.html#E9:32_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E15:32_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="aff_2.html#E9:32_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_2.html#E12:32_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T72">AFF_1:72</a></i>;<br/>
<a NAME="E16:32_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E11:32_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="aff_2.html#E15:32_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T54">AFF_1:54</a></i>;<br/>
<a NAME="E17:32_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E18:32_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:32_1_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E9:32_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_2.html#E15:32_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E2:32_1_3"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:32_1_3"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E4:32_1_3"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E8:32_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E19:32_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32"><i><font color="Green">E15</font></i></a>, <a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E17:32_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_2.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E20:32_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E5:32_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E21:32_1"/><b>then </b>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E2:32_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E7:32_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="aff_2.html#E9:32_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_2.html#E15:32_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="aff_2.html#E17:32_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>
<a NAME="E22:32_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E9:32_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E23:32_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E24:32_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E25:32_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E8:32_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E26:32_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E27:32_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E28:32_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E4:32_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E29:32_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E30:32_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E31:32_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E32:32_1"/><b>then </b>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) &amp; ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) )
 
<b>by </b><i><a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_2.html#E7:32_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E33:32_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_2.html#E1:32_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="aff_2.html#E2:32_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="aff_2.html#E4:32_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="aff_2.html#E6:32_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>


</div><b>end;</b></div>


</div>
