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<b>let </b><font color="Maroon">S</font> be   <a href="incsp_1.html#NM4">IncSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="incsp_1.html#NM3">PLANE</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:65"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font>
 ;<br/>

<b>consider </b><font color="Maroon">L</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:65"/><i><font color="Green">E24</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">L</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>, <font color="Maroon">E</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E5:65"/><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R5" target="_self">on</a> <font color="Maroon">P</font>
 <b>and </b><br/><a NAME="E6:65"/><i><font color="Green">E57</font></i>: 
not <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</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="E7:65"/>
not <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#R4" target="_self">on</a> <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:65"/><b>then </b>
(  not <font color="Maroon">C</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> or  not <font color="Maroon">D</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> or  not <font color="Maroon">E</font> <a href="incsp_1.html#R1" target="_self">on</a> <font color="Maroon">L</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E9:65"/><b>then </b>
( (  not <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>  or  not <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">D</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#NR6" target="_self">is_collinear</a>  or  not <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">E</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#NR6" target="_self">is_collinear</a>  ) &amp; <font color="Maroon">C</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">P</font> &amp; <font color="Maroon">D</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">P</font> &amp; <font color="Maroon">E</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">P</font> )
 
<b>by </b><i>, , , , <a class="txt" href="incsp_1.html#E3:65"><i><font color="Green">E24</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:65"/>
 ex <font color="Olive">C</font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">C</font> <a href="incsp_1.html#R2" target="_self">on</a> <font color="Maroon">P</font> &amp; not <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="Olive">C</font></span><a href="domain_1.html#K8">}</a></span> <a href="incsp_1.html#NR6" target="_self">is_collinear</a>  )
 ;<br/>


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