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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <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>, <font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a> 
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:19"/><i><font color="Green">E21</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E4:19"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E5:19"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E6:19"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E7:19"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E8:19"/><i><font color="Green">E26</font></i>: 
<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>4</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E9:19"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</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>9</sub></font>
 <b>and </b><br/><a NAME="E10:19"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E11:19"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E12:19"/><i><font color="Green">E30</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E13:19"/><i><font color="Green">E31</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E14:19"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E2:19"><i><font color="Green">E20</font></i></a>, <a class="txt" href="translac.html#E3:19"><i><font color="Green">E21</font></i></a>, <a class="txt" href="translac.html#E4:19"><i><font color="Green">E22</font></i></a>, <a class="txt" href="translac.html#E6:19"><i><font color="Green">E24</font></i></a>, <a class="txt" href="translac.html#E8:19"><i><font color="Green">E26</font></i></a>, <a class="txt" href="translac.html#E12:19"><i><font color="Green">E30</font></i></a>, <a class="txt" href="translac.html#E19"><i><font color="Green">Lemma17</font></i></a></i>;<br/>
<a NAME="E15:19"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:19"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</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="translac.html#E4:19"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:19"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E5:19"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E18:19"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E6:19"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E19:19"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E7:19"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E20:19"/><i><font color="Green">E37</font></i>: 
<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>9</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E8:19"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E21:19"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>6</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>4</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E9:19"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E22:19"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E10:19"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E23:19"/><i><font color="Green">E40</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>7</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E11:19"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E24:19"/><i><font color="Green">E41</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E4:19"><i><font color="Green">E22</font></i></a>, <a class="txt" href="translac.html#E6:19"><i><font color="Green">E24</font></i></a>, <a class="txt" href="translac.html#E12:19"><i><font color="Green">E30</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E25:19"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E5:19"><i><font color="Green">E23</font></i></a>, <a class="txt" href="translac.html#E7:19"><i><font color="Green">E25</font></i></a>, <a class="txt" href="translac.html#E13:19"><i><font color="Green">E31</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E26:19"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:19"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E2:19"><i><font color="Green">E20</font></i></a>, <a class="txt" href="translac.html#E15:19"><i><font color="Green">E32</font></i></a>, <a class="txt" href="translac.html#E16:19"><i><font color="Green">E33</font></i></a>, <a class="txt" href="translac.html#E17:19"><i><font color="Green">E34</font></i></a>, <a class="txt" href="translac.html#E18:19"><i><font color="Green">E35</font></i></a>, <a class="txt" href="translac.html#E19:19"><i><font color="Green">E36</font></i></a>, <a class="txt" href="translac.html#E20:19"><i><font color="Green">E37</font></i></a>, <a class="txt" href="translac.html#E21:19"><i><font color="Green">E38</font></i></a>, <a class="txt" href="translac.html#E22:19"><i><font color="Green">E39</font></i></a>, <a class="txt" href="translac.html#E23:19"><i><font color="Green">E40</font></i></a>, <a class="txt" href="translac.html#E24:19"><i><font color="Green">E41</font></i></a>, <a class="txt" href="translac.html#E18"><i><font color="Green">Lemma16</font></i></a></i>;<br/>


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