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

<b>let </b><font color="Maroon">S</font> be   <a href="incsp_1.html#NM4">IncSpace</a>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">P</font> being  <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">S</font>  holds <br/>(  not <font color="Maroon">K</font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Olive">P</font> or  not <font color="Maroon">L</font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Olive">P</font> )
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L</font>
 ;<br/>

<b>consider </b><font color="Maroon">A</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>, <font color="Maroon">B</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E4:36"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E5:36"/><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">K</font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>consider </b><font color="Maroon">C</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>, <font color="Maroon">D</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E7:36"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 <b>and </b><br/><a NAME="E8:36"/><i><font color="Green">E60</font></i>: 
<span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E9:36"/>
( <font color="Maroon">A</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">K</font> &amp; <font color="Maroon">B</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">K</font> &amp; <font color="Maroon">C</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">K</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T14" target="_self">Th14</a>, , <a class="ref" href="incsp_1.html#T17" target="_self">Th17</a>, </i>;<br/>
<a NAME="E10:36"/><b>then </b>
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">K</font>
 
<b>by </b><i/>;<br/>
<a NAME="E11:36"/><b>then </b>
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#NR6" target="_self">is_collinear</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E12:36"/><b>then </b>
<span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</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#E1:36"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">Q</font> being   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E14:36"/><i><font color="Green">E61</font></i>: 
<span class="p1"><a href="domain_1.html#K9">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K9">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">Q</font>
 <b>by </b><i/>;<br/>
<a NAME="E15:36"/>
( <font color="Maroon">A</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">B</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">C</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">D</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">Q</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T18" target="_self">Th18</a>, </i>;<br/>
<a NAME="E16:36"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">Q</font> &amp; <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">Q</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E17:36"/><b>then </b>
( <font color="Maroon">K</font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">L</font> <a href="incsp_1.html#R3" target="_self">on</a> <font color="Maroon">Q</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T15" target="_self">Th15</a>, , <a class="ref" href="incsp_1.html#T16" target="_self">Th16</a>, <a class="ref" href="incsp_1.html#T17" target="_self">Th17</a>, <a class="ref" href="incsp_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E18:36"/>
contradiction
 <b>by </b><i><a class="ref" href="incsp_1.html#T13" target="_self">Th13</a></i>;<br/>


</div>
