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

<b>let </b><font color="Maroon" title="c1">FCPS</font> be  <a href="anproj_2.html#NV10" title="ANPROJ_2:NV.10">up-3-dimensional</a> <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FCPS</font>;<br/>







<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E16">A1</font></i>: 
not <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/>

<b>assume </b><a NAME="E2:20"/><i><font color="Green" title="E17">A2</font></i>: 
for <font color="Olive" title="b1">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FCPS</font> holds  <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Olive" title="b1">s</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FCPS</font><b> such that </b><br/><a NAME="E4:20"/><i><font color="Green" title="E18">A3</font></i>: 
not <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T16" target="_self" title="PROJDES1:th.16">Th16</a></i>;<br/>
<a NAME="E5:20"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c5">a</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c6">b</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c7">c</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font>,<font color="Maroon" title="c8">d</font> <a href="projdes1.html#R1" title="PROJDES1:pred.1">are_coplanar</a>  )
 
<b>by </b><i><a class="txt" href="projdes1.html#E2:20"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:20"/>
contradiction
 <b>by </b><i><a class="txt" href="projdes1.html#E1:20"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="projdes1.html#E4:20"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="projdes1.html#T12" target="_self" title="PROJDES1:th.12">Th12</a></i>;<br/>


</div>
