<?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>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="E1:13"/><i><font color="Green">E14</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> &amp;  <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="E2:13"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a> 
 <b>and </b><br/><a NAME="E3:13"/><i><font color="Green">E16</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>5</sub></font>
 <b>and </b><br/><a NAME="E4:13"/><i><font color="Green">E17</font></i>: 
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( 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="Olive">b<sub>1</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <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>6</sub></font> )
 <b>and </b><br/><a NAME="E5:13"/><i><font color="Green">E18</font></i>: 
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( 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="Olive">b<sub>1</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <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/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</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="E7:13"/><i><font color="Green">E19</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>8</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <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>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>8</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>6</sub></font> &amp;  <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>6</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E4:13"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</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="E9:13"/><i><font color="Green">E20</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>10</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <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> )
 <b>by </b><i><a class="txt" href="homothet.html#E5:13"><i><font color="Green">E18</font></i></a></i>;<br/>
<a NAME="E10:13"/><i><font color="Green">E21</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>8</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>10</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E11:13"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:13_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="txt" href="homothet.html#E5:13"><i><font color="Green">E18</font></i></a>, <a class="txt" href="homothet.html#E12"><i><font color="Green">Lemma12</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:13_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E12:13"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="txt" href="homothet.html#E9"><i><font color="Green">Lemma9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:13_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E5:13"><i><font color="Green">E18</font></i></a>, <a class="txt" href="homothet.html#E1:13_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="homothet.html#E9"><i><font color="Green">Lemma9</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E13:13"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</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>5</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</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>5</sub></font> )
 ;<br/>

<a NAME="E2:13_3"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/>
<a NAME="E3:13_3"/>
 <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>2</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E4:13_3"/><b>then </b><i><font color="Green">E27</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E10:13"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E5:13_3"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_3_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E3:13"><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#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E1:13_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:13_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E1:13_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="homothet.html#E2:13_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="homothet.html#E4:13_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:13"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_4"/><i><font color="Green">E27</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:13_4"/>
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E1:13_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:13_4"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E2:13_4"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/>
<a NAME="E5:13_4"/><i><font color="Green">E29</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:13_4"/>
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E1:13_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:13_4"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E4:13_4"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E5:13_4"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E15:13"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</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>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_5"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</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>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<div><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_5_1"/><i><font color="Green">E28</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/><a NAME="E2:13_5_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</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="homothet.html#E9:13"><i><font color="Green">E20</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="E3:13_5_1"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E10:13"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/><a NAME="E4:13_5_1"/>
<font color="Maroon">c<sub>5</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>9</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E5:13_5_1"/><b>then </b>
<font color="Maroon">c<sub>5</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>11</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E2:13"><i><font color="Green">E15</font></i></a>, <a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E10:13"><i><font color="Green">E21</font></i></a>, <a class="txt" href="homothet.html#E1:13_5"><i><font color="Green">E26</font></i></a>, <a class="txt" href="homothet.html#E1:13_5_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E3:13_5_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="homothet.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E6:13_5_1"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>set </b><font color="Maroon">c<sub>12</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/><b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><a NAME="E7:13_5_1"/><i><font color="Green">E31</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> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</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="E8:13_5_1"/><i><font color="Green">E32</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</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>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>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>2</sub></font>,<font color="Maroon">c<sub>8</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>2</sub></font>,<font color="Maroon">c<sub>8</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>2</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>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E10:13"><i><font color="Green">E21</font></i></a>, <a class="txt" href="homothet.html#E1:13_5_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E3:13_5_1"><i><font color="Green">E29</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="E9:13_5_1"/><i><font color="Green">E33</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_5_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_5_1_1"/><i><font color="Green">E34</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_5_1_1"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</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>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E10:13"><i><font color="Green">E21</font></i></a>, <a class="txt" href="homothet.html#E8:13_5_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E3:13_5_1_1"/><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>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13_5_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/>
<a NAME="E4:13_5_1_1"/><b>then </b>
(  <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> &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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13_5"><i><font color="Green">E26</font></i></a>, <a class="txt" href="homothet.html#E7:13_5_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E8:13_5_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E5:13_5_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:13_5_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E7:13_5_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>hence </b><a NAME="E11:13_5_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E6:13_5_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="homothet.html#E9:13_5_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_5_2"/><i><font color="Green">E28</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/><a NAME="E2:13_5_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</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="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E2:13"><i><font color="Green">E15</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E3:13_5_2"/><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>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_5_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_5_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_5_2_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:13_5_2_1"/>
(  <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>2</sub></font> &amp;  <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>by </b><i><a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E4:13_5_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E1:13_5"><i><font color="Green">E26</font></i></a>, <a class="txt" href="homothet.html#E2:13_5_2_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T20">AFF_1:20</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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>;<br/><a NAME="E4:13_5_2"/><i><font color="Green">E31</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> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="homothet.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</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="E5:13_5_2"/><i><font color="Green">E32</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</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>10</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>2</sub></font>,<font color="Maroon">c<sub>10</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>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E10:13"><i><font color="Green">E21</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="E6:13_5_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E4:13_5_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E7:13_5_2"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E2:13"><i><font color="Green">E15</font></i></a>, <a class="txt" href="homothet.html#E7:13"><i><font color="Green">E19</font></i></a>, <a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E1:13_5_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="homothet.html#E2:13_5_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="homothet.html#E3:13_5_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="homothet.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/><a NAME="E8:13_5_2"/><i><font color="Green">E34</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_5_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_5_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_5_2_2"/><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>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2">AFF_1:def 2</a></i>;<br/>
<a NAME="E3:13_5_2_2"/><b>then </b>
(  <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> &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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:13_5"><i><font color="Green">E26</font></i></a>, <a class="txt" href="homothet.html#E4:13_5_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="homothet.html#E5:13_5_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E4:13_5_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:13_5_2"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="homothet.html#E4:13_5_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>hence </b><a NAME="E10:13_5_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E9:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="homothet.html#E7:13_5_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="homothet.html#E8:13_5_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:13_5"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E2:13_5"><i><font color="Green">E27</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E16:13"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="homothet.html#E11:13"><i><font color="Green">E22</font></i></a>, <a class="txt" href="homothet.html#E12:13"><i><font color="Green">E23</font></i></a>, <a class="txt" href="homothet.html#E13:13"><i><font color="Green">E24</font></i></a>, <a class="txt" href="homothet.html#E14:13"><i><font color="Green">E25</font></i></a></i>;<br/>


</div>
