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

<b>let </b><font color="Maroon">FCPS</font> be  <a href="anproj_2.html#V7">up-3-dimensional</a> <a href="anproj_2.html#NM1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FCPS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FCPS</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FCPS</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FCPS</font>;<br/>









<b>assume </b><a NAME="E1:11"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:11"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:11"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E5:11"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E6:11"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:11"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E8:11"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E9:11"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E10:11"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E11:11"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E12:11"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E13:11"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E14:11"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E15:11"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E16:11"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E17:11"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E18:11"/>
( <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  )
 <b>by </b><i>, , , , , , , , , , , </i>;<br/>


</div>
