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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>assume </b><a NAME="E1:3"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR11" target="_self">satisfies_des</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> 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="E2:3"/><i><font color="Green">E5</font></i>: 
( not <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>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not <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>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>and </b><br/><a NAME="E3:3"/><i><font color="Green">E6</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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E4:3"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<a NAME="E5:3"/><i><font color="Green">E8</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>by </b><i><a class="txt" href="pardepap.html#E2:3"><i><font color="Green">E5</font></i></a>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E6:3"/><i><font color="Green">E9</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="pardepap.html#E5:3"><i><font color="Green">E8</font></i></a>, <a class="ref" href="aff_1.html#T26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<a NAME="E7:3"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</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="E9:3"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E10:3"/><i><font color="Green">E12</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="pardepap.html#E6:3"><i><font color="Green">E9</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</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="E12:3"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E13:3"/><i><font color="Green">E14</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="pardepap.html#E6:3"><i><font color="Green">E9</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/>
<a NAME="E14:3"/><i><font color="Green">E15</font></i>: 
( <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>10</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 
<b>by </b><i><a class="txt" href="pardepap.html#E10:3"><i><font color="Green">E12</font></i></a>, <a class="txt" href="pardepap.html#E13:3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/>
<a NAME="E15:3"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="pardepap.html#E7:3"><i><font color="Green">E10</font></i></a>, <a class="txt" href="pardepap.html#E10:3"><i><font color="Green">E12</font></i></a>, <a class="txt" href="pardepap.html#E13:3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T57">AFF_1:57</a></i>;<br/>
<a NAME="E16:3"/><b>then </b>
( <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>9</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="pardepap.html#E3:3"><i><font color="Green">E6</font></i></a>, <a class="txt" href="pardepap.html#E5:3"><i><font color="Green">E8</font></i></a>, <a class="ref" href="aff_1.html#T46">AFF_1:46</a></i>;<br/>
<a NAME="E17:3"/><b>then </b><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="pardepap.html#E9:3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="pardepap.html#E12:3"><i><font color="Green">E13</font></i></a>, <a class="txt" href="pardepap.html#E14:3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<a NAME="E18:3"/><i><font color="Green">E17</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="pardepap.html#E2:3"><i><font color="Green">E5</font></i></a>, <a class="txt" href="pardepap.html#E6:3"><i><font color="Green">E9</font></i></a>, <a class="txt" href="pardepap.html#E9:3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<a NAME="E19:3"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="pardepap.html#E2:3"><i><font color="Green">E5</font></i></a>, <a class="txt" href="pardepap.html#E6:3"><i><font color="Green">E9</font></i></a>, <a class="txt" href="pardepap.html#E12:3"><i><font color="Green">E13</font></i></a>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<b>hence </b><a NAME="E20:3"/>
<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>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="pardepap.html#E1:3"><i><font color="Green">E4</font></i></a>, <a class="txt" href="pardepap.html#E4:3"><i><font color="Green">E7</font></i></a>, <a class="txt" href="pardepap.html#E6:3"><i><font color="Green">E9</font></i></a>, <a class="txt" href="pardepap.html#E9:3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="pardepap.html#E10:3"><i><font color="Green">E12</font></i></a>, <a class="txt" href="pardepap.html#E12:3"><i><font color="Green">E13</font></i></a>, <a class="txt" href="pardepap.html#E13:3"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pardepap.html#E14:3"><i><font color="Green">E15</font></i></a>, <a class="txt" href="pardepap.html#E17:3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="pardepap.html#E18:3"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_2.html#D11">AFF_2:def 11</a></i>;<br/>


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