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<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">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FCPS</font>;<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">d</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>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FCPS</font>;<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>assume </b><a NAME="E1:5"/><i><font color="Green">E25</font></i>: 
( not <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">o</font>,<font color="Maroon">d</font>,<font color="Maroon">d'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">s</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d'</font> &amp; <font color="Maroon">a'</font>,<font color="Maroon">d'</font>,<font color="Maroon">s</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a'</font> )
 ;<br/>

<b>assume </b><a NAME="E2:5"/>
not <font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E3:5"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">d'</font>,<font color="Maroon">a'</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:5"/>
<font color="Maroon">d</font>,<font color="Maroon">d'</font>,<font color="Maroon">o</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:5"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">o</font>,<font color="Maroon">a'</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, , <a class="ref" href="collsp.html#T11">COLLSP:11</a></i>;<br/>
<a NAME="E6:5"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a'</font>,<font color="Maroon">d</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:5"/>
<font color="Maroon">o</font>,<font color="Maroon">a'</font>,<font color="Maroon">a</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:5"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="collsp.html#T11">COLLSP:11</a></i>;<br/>


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