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<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>, <font color="Maroon" title="c6">e</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="E1:10"/><i><font color="Green" title="E9">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="c4">c</font>,<font color="Maroon" title="c6">e</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="c6">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> )
 ;<br/>

<b>assume </b><a NAME="E2:10"/>
<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 ;<br/>

<a NAME="E3:10"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c2">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/>
<a NAME="E4:10"/><b>then </b>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:10"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>;<br/>
<a NAME="E5:10"/><b>then </b>
( <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>  &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>  )
 
<b>by </b><i><a class="txt" href="hessenbe.html#E1:10"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="hessenbe.html#T3" target="_self" title="HESSENBE:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E6:10"/>
contradiction
 <b>by </b><i><a class="txt" href="hessenbe.html#E1:10"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="hessenbe.html#T4" target="_self" title="HESSENBE:th.4">Th4</a></i>;<br/>


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