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<b>let </b><font color="Maroon">S</font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/>

<b>assume </b><a NAME="E2:47"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Olive">z</font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 ;<br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E4:47"/><i><font color="Green">E27</font></i>: 
not <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/>
<a NAME="E5:47"/>
( <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">a</font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">b</font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:47"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


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