<?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> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:34"/><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>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>5</sub></font> )
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green">E26</font></i>: 
not <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">c<sub>5</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="E3:34"/><i><font color="Green">E27</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/>

<a NAME="E4:34"/>
<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>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E3:34"><i><font color="Green">E27</font></i></a>, <a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/>
<a NAME="E5:34"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E6:34"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>hence </b><a NAME="E7:34"/>
contradiction
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:34"><i><font color="Green">E26</font></i></a>, <a class="txt" href="incsp_1.html#E3:34"><i><font color="Green">E27</font></i></a>, <a class="ref" href="incsp_1.html#T12" target="_self">Th12</a></i>;<br/>


</div>
