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<b>let </b><font color="Maroon">CS</font> be  <a href="anproj_2.html#V7">up-3-dimensional</a> <a href="anproj_2.html#NM1">CollProjectiveSpace</a>;<br/>

<a NAME="E1:31"/>
for <font color="Olive">o</font>, <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">a'</font>, <font color="Olive">b'</font>, <font color="Olive">c'</font>, <font color="Olive">r</font>, <font color="Olive">q</font>, <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>  st <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">a'</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">a'</font> &amp; <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b'</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b'</font> &amp; <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c'</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c'</font> &amp; not <font color="Olive">o</font>,<font color="Olive">a</font>,<font color="Olive">b</font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Olive">o</font>,<font color="Olive">a</font>,<font color="Olive">c</font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Olive">o</font>,<font color="Olive">b</font>,<font color="Olive">c</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">p</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">a'</font>,<font color="Olive">b'</font>,<font color="Olive">p</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">b'</font>,<font color="Olive">c'</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">a</font>,<font color="Olive">c</font>,<font color="Olive">q</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">a'</font>,<font color="Olive">c'</font>,<font color="Olive">q</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">a</font>,<font color="Olive">a'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">b</font>,<font color="Olive">b'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">c</font>,<font color="Olive">c'</font> <a href="collsp.html#R1">is_collinear</a>  holds <br/><font color="Olive">r</font>,<font color="Olive">q</font>,<font color="Olive">p</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:31"/>
<font color="Maroon">CS</font> is <a href="anproj_2.html#V5">Desarguesian</a>
 <b>by </b><i><a class="ref" href="anproj_2.html#D12">ANPROJ_2:def 12</a></i>;<br/>


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