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

<b>let </b><font color="Maroon" title="c1">PCPP</font> be   <a href="anproj_2.html#NM1" title="ANPROJ_2:NM.1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PCPP</font>;<br/>









<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E6">A1</font></i>: 
( not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:7"/><i><font color="Green" title="E7">A2</font></i>: 
not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font>
 ;<br/>

<a NAME="E3:7"/>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:7"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a>, <a class="ref" href="anproj_2.html#D7" title="ANPROJ_2:def.7">ANPROJ_2:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:7"/>
contradiction
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:7"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="hessenbe.html#E2:7"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="anproj_2.html#D8" title="ANPROJ_2:def.8">ANPROJ_2:def 8</a></i>;<br/>


</div>
