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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:47"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:47"/><i><font color="Green">E32</font></i>: 
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="diraf.html#NR4" target="_self">is_collinear</a> 
 <b>by </b><i><a class="ref" href="diraf.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E5:47"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="diraf.html#NR4" target="_self">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="diraf.html#E2:47"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:47"/>
contradiction
 <b>by </b><i><a class="txt" href="diraf.html#E1:47"><i><font color="Green">E30</font></i></a>, <a class="txt" href="diraf.html#E4:47"><i><font color="Green">E32</font></i></a>, <a class="ref" href="diraf.html#T38" target="_self">Th38</a></i>;<br/>


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