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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="incsp_1.html#NM4">IncSpace</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> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>given </b><font color="Maroon">c<sub>6</sub></font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:33"/><i><font color="Green">E24</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="incsp_1.html#D6" target="_self">INCSP_1:def 6</a><br/>

<b>assume </b><a NAME="E2:33"/><i><font color="Green">E25</font></i>: 
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><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></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#NR7" target="_self">is_coplanar</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:33"/><i><font color="Green">E26</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E5:33"/>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:33"><i><font color="Green">E24</font></i></a>, <a class="txt" href="incsp_1.html#E4:33"><i><font color="Green">E26</font></i></a>, <a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/>
<a NAME="E6:33"/><b>then </b>
( <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; <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E2:33"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incsp_1.html#T18" target="_self">Th18</a>, <a class="ref" href="incsp_1.html#T21" target="_self">Th21</a>, <a class="ref" href="incsp_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E7:33"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E8:33"/><b>then </b>
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:33"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incsp_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E9:33"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E4:33"><i><font color="Green">E26</font></i></a>, <a class="ref" href="incsp_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E10:33"/><b>then </b>
<span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><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></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><a NAME="E11:33"/>
contradiction
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:33"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self">Def7</a></i>;<br/>


</div>
