<?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="E1:22"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_3.html#NR3" target="_self">satisfies_DES1_2</a> 
 ;<br/>

<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#D4">AFF_2:def 4</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><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>, <font color="Maroon">c<sub>11</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="E2:22"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</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>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</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; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green">E11</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="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>and </b><br/><a NAME="E4:22"/><i><font color="Green">E12</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> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E5:22"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>6</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> &amp; <font color="Maroon">c<sub>6</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>11</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1"/><i><font color="Green">E14</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>
 ;<br/><a NAME="E2:22_1"/><b>then </b><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <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="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><a NAME="E3:22_1"/><i><font color="Green">E16</font></i>: 
( not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; not  <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>8</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_1"/><i><font color="Green">E17</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> or  <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>8</sub></font> )
 ;<br/>

<div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:22_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E3:22_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_1_2"/>
 <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>8</sub></font>
 ;<br/><a NAME="E2:22_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>8</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_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E3:22_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E1:22_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1_1"><i><font color="Green">E18</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:22_1"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> implies <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>11</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:22_1_2"/>
(  <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> &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>11</sub></font> &amp; not  <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>8</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E3:22_1_2"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T69">AFF_1:69</a></i>;<br/>
<a NAME="E4:22_1_2"/>
(  <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> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; not  <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>7</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E5:22_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T69">AFF_1:69</a></i>;<br/>
<b>hence </b><a NAME="E6:22_1_2"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E3:22_1_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:22_1"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> implies <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>11</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_3"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:22_1_3"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp;  <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> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</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>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_3"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E4:22_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T69">AFF_1:69</a></i>;<br/>


</div><b>end;</b></div><a NAME="E6:22_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> implies <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>11</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_4"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:22_1_4"/>
(  <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>11</sub></font> &amp;  <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> &amp; not  <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> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_4"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E4:22_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_4"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T69">AFF_1:69</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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><a NAME="E7:22_1"/><i><font color="Green">E20</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <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>6</sub></font>,<font color="Maroon">c<sub>8</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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</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="E8:22_1"/><i><font color="Green">E21</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> implies <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>11</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_5"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:22_1_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:22_1_5"/><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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/>
<a NAME="E4:22_1_5"/><b>then </b>
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T71">AFF_1:71</a></i>;<br/>
<a NAME="E5:22_1_5"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</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>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="aff_1.html#T43">AFF_1:43</a></i>;<br/>
<a NAME="E6:22_1_5"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="aff_1.html#T46">AFF_1:46</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="E8:22_1_5"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</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_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/>
<a NAME="E9:22_1_5"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i><a class="txt" href="aff_3.html#E8:22_1_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/>
<a NAME="E10:22_1_5"/>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E6:22_1_5"><i><font color="Green">E23</font></i></a>, <a class="txt" href="aff_3.html#E8:22_1_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T57">AFF_1:57</a></i>;<br/>
<a NAME="E11:22_1_5"/><b>then </b>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E8:22_1_5"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_3.html#E9:22_1_5"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<b>hence </b><a NAME="E12:22_1_5"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1_5"><i><font color="Green">E22</font></i></a>, <a class="txt" href="aff_3.html#E8:22_1_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:22_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> implies <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>11</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_6"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:22_1_6"/><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> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</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> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E3:22_1_6"/><b>then </b>
(  <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>11</sub></font> &amp; not  <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>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E4:22_1_6"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>
<b>hence </b><a NAME="E5:22_1_6"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E1:22_1_6"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>


</div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_7"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 ;<br/><a NAME="E2:22_1_7"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><b>assume </b><a NAME="E3:22_1_7"/>
not <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>11</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>13</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="E5:22_1_7"/><i><font color="Green">E25</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>14</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="E7:22_1_7"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/><a NAME="E8:22_1_7"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/><a NAME="E9:22_1_7"/>
not <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>14</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_1"/>
<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>14</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T57">AFF_1:57</a></i>;<br/>
<a NAME="E3:22_1_7_1"/><b>then </b>
<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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<b>hence </b><a NAME="E4:22_1_7_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>15</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="E11:22_1_7"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E8:22_1_7"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>set </b><font color="Maroon">c<sub>16</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>;<br/><a NAME="E12:22_1_7"/><i><font color="Green">E29</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &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>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</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="E13:22_1_7"/><i><font color="Green">E30</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T51">AFF_1:51</a></i>;<br/><a NAME="E14:22_1_7"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/><a NAME="E15:22_1_7"/><i><font color="Green">E32</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:22_1_7_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/>
<a NAME="E4:22_1_7_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<a NAME="E5:22_1_7_2"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E13:22_1_7"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T57">AFF_1:57</a></i>;<br/>
<a NAME="E6:22_1_7_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:22_1_7_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_3.html#E5:22_1_7_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T46">AFF_1:46</a></i>;<br/>
<a NAME="E8:22_1_7_2"/><b>then </b>
<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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<b>hence </b><a NAME="E9:22_1_7_2"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>


</div><b>end;</b></div><a NAME="E16:22_1_7"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_3"/><b>then </b>
( not  <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>7</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_7_3"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:22_1_7"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_4"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_4"/><b>then </b>
( not  <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> &amp;  <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> &amp; <font color="Maroon">c<sub>8</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> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E3:22_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E3:22_1_7_4"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E16:22_1_7"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E18:22_1_7"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><a NAME="E19:22_1_7"/>
not <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_5"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="aff_1.html#R2">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_5"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E14:22_1_7"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T57">AFF_1:57</a></i>;<br/>
<a NAME="E3:22_1_7_5"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T48">AFF_1:48</a></i>;<br/>
<a NAME="E4:22_1_7_5"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E8:22_1_7"><i><font color="Green">E27</font></i></a>, <a class="txt" href="aff_3.html#E11:22_1_7"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/>
<div><i><font color="Green">E37</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_7_5_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><a NAME="E2:22_1_7_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E3:22_1_7_5_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E4:22_1_7_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_7_5_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><a NAME="E2:22_1_7_5_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E3:22_1_7_5_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="txt" href="aff_3.html#E8:22_1_7"><i><font color="Green">E27</font></i></a>, <a class="txt" href="aff_3.html#E4:22_1_7_5"><i><font color="Green">E36</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7_5_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E4:22_1_7_5_2"/><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>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E14:22_1_7"><i><font color="Green">E31</font></i></a>, <a class="txt" href="aff_3.html#E4:22_1_7_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><b>hence </b><a NAME="E5:22_1_7_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E15:22_1_7"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:22_1_7_5"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7_5"><i><font color="Green">E37</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>17</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="E21:22_1_7"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><a NAME="E22:22_1_7"/><i><font color="Green">E37</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E21:22_1_7"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E23:22_1_7"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_6"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_6"/><b>then </b>
( <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>6</sub></font>,<font color="Maroon">c<sub>8</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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E13:22_1_7"><i><font color="Green">E30</font></i></a>, <a class="txt" href="aff_3.html#E21:22_1_7"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>
<a NAME="E3:22_1_7_6"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E16:22_1_7"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E4:22_1_7_6"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>


</div><b>end;</b></div><b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><a NAME="E24:22_1_7"/><i><font color="Green">E39</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <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>17</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E23:22_1_7"><i><font color="Green">E38</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="E25:22_1_7"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_7"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_7"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</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>15</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="txt" href="aff_3.html#E11:22_1_7"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E3:22_1_7_7"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E4:22_1_7_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7_7"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:22_1_7_7"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E6:22_1_7_7"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>


</div><b>end;</b></div><a NAME="E26:22_1_7"/><i><font color="Green">E41</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1_7_8"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 ;<br/>

<a NAME="E2:22_1_7_8"/><b>then </b><i><font color="Green">E42</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E21:22_1_7"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E3:22_1_7_8"/><b>then </b><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_7_8_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><a NAME="E2:22_1_7_8_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E21:22_1_7"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/><a NAME="E3:22_1_7_8_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/><a NAME="E4:22_1_7_8_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="txt" href="aff_3.html#E8:22_1_7"><i><font color="Green">E27</font></i></a>, <a class="txt" href="aff_3.html#E11:22_1_7"><i><font color="Green">E28</font></i></a>, <a class="txt" href="aff_3.html#E25:22_1_7"><i><font color="Green">E40</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E5:22_1_7_8_1"/><b>then </b>
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E14:22_1_7"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><a NAME="E6:22_1_7_8_1"/><b>then </b><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_7_8_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_7_8_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:22_1_7_8_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E3:22_1_7_8_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E17:22_1_7"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E4:22_1_7_8_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:22_1_7_8_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E6:22_1_7_8_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:22_1_7_8"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</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>by </b><i><a class="txt" href="aff_3.html#E3:22_1_7_8"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:22_1_7_8"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</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="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:22_1_7_8"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</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>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:22_1_7_8"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E2:22_1_7_8"><i><font color="Green">E42</font></i></a>, <a class="txt" href="aff_3.html#E4:22_1_7_8"><i><font color="Green">E44</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E9:22_1_7_8"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:22_1_7_8"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:22_1_7_8"/><b>then </b>
<font color="Maroon">c<sub>6</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>11</sub></font>
 
<b>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E12:22_1_7_8"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</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>by </b><i><a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1_7_8"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E13:22_1_7_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E14:22_1_7_8"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div><a NAME="E27:22_1_7"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E13:22_1_7"><i><font color="Green">E30</font></i></a>, <a class="txt" href="aff_3.html#E21:22_1_7"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E28:22_1_7"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1_7"><i><font color="Green">E26</font></i></a>, <a class="txt" href="aff_3.html#E11:22_1_7"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E29:22_1_7"/>
( not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E1:22_1_7"><i><font color="Green">E23</font></i></a>, <a class="txt" href="aff_3.html#E11:22_1_7"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E30:22_1_7"/><b>then </b>
<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>17</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E1:22"><i><font color="Green">E9</font></i></a>, <a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E1:22_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="aff_3.html#E5:22_1_7"><i><font color="Green">E25</font></i></a>, <a class="txt" href="aff_3.html#E22:22_1_7"><i><font color="Green">E37</font></i></a>, <a class="txt" href="aff_3.html#E23:22_1_7"><i><font color="Green">E38</font></i></a>, <a class="txt" href="aff_3.html#E24:22_1_7"><i><font color="Green">E39</font></i></a>, <a class="txt" href="aff_3.html#E25:22_1_7"><i><font color="Green">E40</font></i></a>, <a class="txt" href="aff_3.html#E26:22_1_7"><i><font color="Green">E41</font></i></a>, <a class="txt" href="aff_3.html#E27:22_1_7"><i><font color="Green">E42</font></i></a>, <a class="txt" href="aff_3.html#E28:22_1_7"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_3.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E31:22_1_7"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>17</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_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E24:22_1_7"><i><font color="Green">E39</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><a NAME="E32:22_1_7"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E7:22_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="aff_3.html#E13:22_1_7"><i><font color="Green">E30</font></i></a>, <a class="txt" href="aff_3.html#E18:22_1_7"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><a NAME="E33:22_1_7"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E12:22_1_7"><i><font color="Green">E29</font></i></a>, <a class="txt" href="aff_3.html#E21:22_1_7"><i><font color="Green">E36</font></i></a>, <a class="txt" href="aff_3.html#E31:22_1_7"><i><font color="Green">E44</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><b>set </b><font color="Maroon">c<sub>19</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>20</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/><a NAME="E34:22_1_7"/><i><font color="Green">E46</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</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>10</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>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <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>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>10</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>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_3.html#E11:22_1_7"><i><font color="Green">E28</font></i></a>, <a class="txt" href="aff_3.html#E22:22_1_7"><i><font color="Green">E37</font></i></a>, <a class="txt" href="aff_3.html#E33:22_1_7"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D2">AFF_1:def 2</a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/><a NAME="E35:22_1_7"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E5:22"><i><font color="Green">E13</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="aff_3.html#E2:22_1_7"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T51">AFF_1:51</a></i>;<br/><a NAME="E36:22_1_7"/><b>then </b>
( <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>7</sub></font>,<font color="Maroon">c<sub>6</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>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="aff_3.html#E34:22_1_7"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/><a NAME="E37:22_1_7"/><b>then </b>
<font color="Maroon">c<sub>7</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_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E16:22_1_7"><i><font color="Green">E33</font></i></a>, <a class="txt" href="aff_3.html#E34:22_1_7"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><b>hence </b><a NAME="E38:22_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="txt" href="aff_3.html#E4:22"><i><font color="Green">E12</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E11:22_1"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E4:22_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="aff_3.html#E5:22_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="aff_3.html#E6:22_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="aff_3.html#E8:22_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="aff_3.html#E9:22_1"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:22"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="aff_3.html#E2:22"><i><font color="Green">E10</font></i></a>, <a class="txt" href="aff_3.html#E3:22"><i><font color="Green">E11</font></i></a>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>


</div>
