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

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="collsp.html#NM2">CollSp</a>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>







<b>assume </b><a NAME="E1:14"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 ;<br/>

<b>thus </b><a NAME="E2:14"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<a NAME="E1:14_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  ) )
 
<b>by </b><i><a class="txt" href="collsp.html#E1:14"><i><font color="Green">E12</font></i></a>, <a class="ref" href="collsp.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E2:14_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#T7" target="_self">Th7</a>, <a class="ref" href="collsp.html#T8" target="_self">Th8</a></i>;<br/>


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

<b>thus </b><a NAME="E3:14"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><b>proof </b></a><div class="add">

<a NAME="E1:14_2"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  ) )
 
<b>by </b><i><a class="txt" href="collsp.html#E1:14"><i><font color="Green">E12</font></i></a>, <a class="ref" href="collsp.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E2:14_2"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#T7" target="_self">Th7</a>, <a class="ref" href="collsp.html#T8" target="_self">Th8</a></i>;<br/>


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


</div>
