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<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/>

<b>assume </b><a NAME="E1:65"/>
<font color="Maroon">AS</font> is  not   <a href="diraf.html#NM2">AffinPlane</a>
 ;<br/>

<a NAME="E2:65"/><b>then </b>
for <font color="Olive">A</font>, <font color="Olive">P</font>, <font color="Olive">C</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><br/> for <font color="Olive">q</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> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> &amp; <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">P</font> &amp; <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> &amp; <font color="Olive">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">a</font> &amp; <font color="Olive">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> &amp; <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">P</font> &amp; <font color="Olive">b'</font> <a href="hidden.html#R2">in</a> <font color="Olive">P</font> &amp; <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> &amp; <font color="Olive">c'</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> &amp; <font color="Olive">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Olive">P</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Olive">C</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Olive">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">P</font> &amp; <font color="Olive">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">C</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font>
 
<b>by </b><i><a class="ref" href="aff_4.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E3:65"/>
<font color="Maroon">AS</font> is <a href="aff_2.html#V4">Desarguesian</a>
 <b>by </b><i><a class="ref" href="aff_2.html#D4">AFF_2:def 4</a></i>;<br/>


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