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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="anproj_2.html#V6">Pappian</a> <a href="anproj_2.html#NM2">CollProjectivePlane</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



















<b>assume </b><a NAME="E1:16"/><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>4</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>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>7</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>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/>
<div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_1"/><i><font color="Green">E19</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="E2:16_1_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E3:16_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E4:16_1_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E5:16_1_1"/><i><font color="Green">E21</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E6:16_1_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E7:16_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E4:16_1_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="hessenbe.html#E5:16_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/><a NAME="E8:16_1_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E9:16_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E10:16_1_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E11:16_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E12:16_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E13:16_1_1"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E14:16_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E7:16_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="hessenbe.html#E9:16_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="hessenbe.html#E12:16_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E15:16_1_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E2:16_1_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_1_2_1"/><i><font color="Green">E22</font></i>: 
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_1_2_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_1_2_1"/><b>then </b>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E4:16_1_2_1"/><b>then </b><i><font color="Green">E23</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_1_2_1"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:16_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E7:16_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E8:16_1_2_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E4:16_1_2_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_1_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_1_2_2"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_1_2_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_1_2_2"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:16_1_2_2"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E5:16_1_2_2"/><b>then </b><i><font color="Green">E23</font></i>: 
not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:16_1_2_2"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E7:16_1_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E3:16_1_2_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="hessenbe.html#E5:16_1_2_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:16_1_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_3"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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> )
 ;<br/><a NAME="E2:16_1_3"/>
( <font color="Maroon">c<sub>2</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#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:16_1_3_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_1_3_1_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E2:16_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_1_3_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E6:16_1_3_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E7:16_1_3_1_1"/>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b><a NAME="E8:16_1_3_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E6:16_1_3_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>thus </b><a NAME="E2:16_1_3_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_1_3_1_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_1_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_1_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_1_3_1_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:16_1_3_1_2"/>
( not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:16_1_3_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E3:16_1_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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


</div><b>end;</b></div><b>hence </b><a NAME="E3:16_1_3"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:16_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E2:16_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_1"><i><font color="Green">E19</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:16_2_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:16_2_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_2_1_1_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:16_2_1_1_1_1"/>
not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_1_1_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>thus </b><a NAME="E2:16_2_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_2_1_1_1_2"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:16_2_1_1_1_2"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="hessenbe.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_1_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_1_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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


</div><b>end;</b></div><b>hence </b><a NAME="E3:16_2_1_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:16_2_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:16_2_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_2_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_2_1_1"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_1_2_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_1_2_1_1"/>
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_2_1_1_1"/><i><font color="Green">E25</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_2_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_1_2_1_1_1"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_2_1_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E4:16_2_1_2_1_1_1"/>
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:16_2_1_2_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_1_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="hessenbe.html#E4:16_2_1_2_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>thus </b><a NAME="E2:16_2_1_2_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E2:16_2_1_2_1_2"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_1_2_1_2"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_2_1_2_1"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E2:16_2_1_2_1_2_1"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16_2_1_2_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16_2_1_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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


</div><b>end;</b></div><b>hence </b><a NAME="E3:16_2_1_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_1_3"/><i><font color="Green">E22</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>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><a NAME="E2:16_2_1_3"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_3_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_3_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_2_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_1_3_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_1_3_1"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_3_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_3_1_1"/><i><font color="Green">E25</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_3_1_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_1_3_1_1"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_3_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E4:16_2_1_3_1_1"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:16_2_1_3_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E4:16_2_1_3_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_2_1_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_3_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_1_3_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_1_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_2_1_3_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_1_3_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_1_3_2"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E6:16_2_1_3_2"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E7:16_2_1_3_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E4:16_2_1_3_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:16_2_1_3"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E2:16_2_1_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:16_2_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E2:16_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_1"><i><font color="Green">E21</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_2"/><i><font color="Green">E19</font></i>: 
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_2_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  or <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  or <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_2_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:16_2_2_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:16_2_2_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E2:16_2_2_1_1_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_2_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/>
<a NAME="E4:16_2_2_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16_2_2_1_1_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E5:16_2_2_1_1_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:16_2_2_1_1_1_1"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E7:16_2_2_1_1_1_1"/><b>then </b>
( not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E8:16_2_2_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E5:16_2_2_1_1_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>thus </b><a NAME="E2:16_2_2_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_1_1_1_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/>
<a NAME="E2:16_2_2_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_2_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_2_1_1_1_2"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_2_1_1_1_2"/>
not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E6:16_2_2_1_1_1_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E4:16_2_2_1_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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


</div><b>end;</b></div><b>hence </b><a NAME="E3:16_2_2_1_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_2_1_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:16_2_2_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:16_2_2_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_1_2_1_1"/><i><font color="Green">E25</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>7</sub></font>
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/>
<a NAME="E2:16_2_2_1_2_1_1"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_2_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_2_1_2_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_2_1_2_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_2_1_2_1_1"/>
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E6:16_2_2_1_2_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E4:16_2_2_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>thus </b><a NAME="E2:16_2_2_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_1_2_1_2"/><i><font color="Green">E25</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>6</sub></font>
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/>
<a NAME="E2:16_2_2_1_2_1_2"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_2_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_2_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_2_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E6:16_2_2_1_2_1_2"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E7:16_2_2_1_2_1_2"/>
( not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E8:16_2_2_1_2_1_2"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E9:16_2_2_1_2_1_2"/><b>then </b>
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E10:16_2_2_1_2_1_2"/>
<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="hessenbe.html#E6:16_2_2_1_2_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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


</div><b>end;</b></div><b>hence </b><a NAME="E3:16_2_2_1_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_2_1_3"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:16_2_2_1_3"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_3_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:16_2_2_1_3_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_3_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_1_3_1_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E2:16_2_2_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E3:16_2_2_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E4:16_2_2_1_3_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E5:16_2_2_1_3_1_1"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E6:16_2_2_1_3_1_1"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E7:16_2_2_1_3_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E4:16_2_2_1_3_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>thus </b><a NAME="E2:16_2_2_1_3_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1_3_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_1_3_1_2"/>
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_1_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:16_2_2_1_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:16_2_2_1_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E4:16_2_2_1_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E5:16_2_2_1_3_1_2"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:16_2_2_1_3_1_2"/>
( not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E7:16_2_2_1_3_1_2"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E8:16_2_2_1_3_1_2"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E9:16_2_2_1_3_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="hessenbe.html#E5:16_2_2_1_3_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="hessenbe.html#T9" target="_self">Th9</a></i>;<br/>


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


</div><b>end;</b></div><b>hence </b><a NAME="E3:16_2_2_1_3"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:16_2_2_1"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16_2_2_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="hessenbe.html#E2:16_2_2_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_2_1"><i><font color="Green">E23</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_2_2"/><i><font color="Green">E21</font></i>: 
( not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/><b>consider </b><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="E3:16_2_2_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D14">ANPROJ_2:def 14</a></i>;<br/><a NAME="E4:16_2_2_2"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_2_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E2:16_2_2_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>

<a NAME="E3:16_2_2_2_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E4:16_2_2_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>

<b>thus </b><a NAME="E5:16_2_2_2_1"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="hessenbe.html#E3:16_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:16_2_2_2"/>
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2_2_2"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="hessenbe.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E2:16_2_2_2_2"/>
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:16_2_2_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="hessenbe.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="hessenbe.html#E1:16_2_2_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="hessenbe.html#E3:16_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="hessenbe.html#E4:16_2_2_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="anproj_2.html#D13">ANPROJ_2:def 13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:16_2_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E2:16_2_2"><i><font color="Green">E20</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:16_2"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E2:16_2"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:16"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="hessenbe.html#E3:16"><i><font color="Green">E16</font></i></a></i>;<br/>


</div>
