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

<b>let </b><font color="Maroon">c<sub>10</sub></font> be  <a href="collsp.html#V4" target="_self">proper</a> <a href="collsp.html#NM2">CollSp</a>;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="collsp.html#M2" target="_self">LINE</a> of <font color="Maroon">c<sub>10</sub></font>;<br/>









<b>assume </b><a NAME="E1:33"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font><b> such that </b><br/><a NAME="E3:33"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font>
 <b>and </b><br/><a NAME="E4:33"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="collsp.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="collsp.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E5:33"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font> : <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  </span>}</span> 
 
<b>by </b><i><a class="txt" href="collsp.html#E1:33"><i><font color="Green">E26</font></i></a>, <a class="txt" href="collsp.html#E4:33"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E6:33"/><b>then </b><i><font color="Green">E29</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  )
 
;<br/>
<a NAME="E7:33"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font> : <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  </span>}</span> 
 
<b>by </b><i><a class="txt" href="collsp.html#E1:33"><i><font color="Green">E26</font></i></a>, <a class="txt" href="collsp.html#E4:33"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E8:33"/><b>then </b><i><font color="Green">E30</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  )
 
;<br/>
<a NAME="E9:33"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font> : <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  </span>}</span> 
 
<b>by </b><i><a class="txt" href="collsp.html#E1:33"><i><font color="Green">E26</font></i></a>, <a class="txt" href="collsp.html#E4:33"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E10:33"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  )
 
;<br/>
<b>hence </b><a NAME="E11:33"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i><a class="txt" href="collsp.html#E3:33"><i><font color="Green">E27</font></i></a>, <a class="txt" href="collsp.html#E6:33"><i><font color="Green">E29</font></i></a>, <a class="txt" href="collsp.html#E8:33"><i><font color="Green">E30</font></i></a>, <a class="ref" href="collsp.html#T8" target="_self">Th8</a></i>;<br/>


</div>
