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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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</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="E1:42"/><i><font color="Green">E29</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> &amp; <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>  )
 ;<br/>

<div><i><font color="Green">E30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:42_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:42"><i><font color="Green">E29</font></i></a>, <a class="ref" href="diraf.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:42_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T28" target="_self">Th28</a></i>;<br/><b>hence </b><a NAME="E4:42_1"/>
<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#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:42_2"/><i><font color="Green">E31</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>4</sub></font>
 ;<br/><a NAME="E2:42_2"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:42"><i><font color="Green">E29</font></i></a>, <a class="ref" href="diraf.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:42_2"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:42"><i><font color="Green">E29</font></i></a>, <a class="ref" href="diraf.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E4:42_2"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T26" target="_self">Th26</a></i>;<br/><a NAME="E5:42_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="diraf.html#E1:42_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="diraf.html#T28" target="_self">Th28</a></i>;<br/><b>hence </b><a NAME="E6:42_2"/>
<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#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:42"/>
<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="txt" href="diraf.html#E2:42"><i><font color="Green">E30</font></i></a></i>;<br/>


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