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



<b>consider </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:75"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:75"/><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</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>2</sub></font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:75"/><i><font color="Green">E48</font></i>: 
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><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></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#NR7" target="_self">is_coplanar</a> 
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:75"><i><font color="Green">E46</font></i></a>, <a class="ref" href="incsp_1.html#T77" target="_self">Th77</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>7</sub></font> =  <a href="incsp_1.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>

<b>given </b><font color="Maroon">c<sub>8</sub></font> being   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E6:75"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E7:75"/>
not <span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#NR7" target="_self">is_coplanar</a> 
 
<b>by </b><i><a class="txt" href="incsp_1.html#E5:75"><i><font color="Green">E48</font></i></a>, <a class="ref" href="enumset1.html#T118">ENUMSET1:118</a></i>;<br/>
<a NAME="E8:75"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E9:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</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>7</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E10:75"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</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>8</sub></font> &amp; <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</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>8</sub></font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E3:75"><i><font color="Green">E47</font></i></a>, <a class="txt" href="incsp_1.html#E6:75"><i><font color="Green">E49</font></i></a>, <a class="ref" href="incsp_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E11:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</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#K7">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</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>8</sub></font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E12:75"/><b>then </b>
<span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><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></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>;<br/>
<b>hence </b><a NAME="E13:75"/>
contradiction
 <b>by </b><i><a class="txt" href="incsp_1.html#E5:75"><i><font color="Green">E48</font></i></a>, <a class="ref" href="incsp_1.html#D7" target="_self">Def7</a></i>;<br/>


</div>
