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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM1">AffinSpace</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> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:59"/>
<font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>and </b><br/><a NAME="E2:59"/>
<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>and </b><br/><a NAME="E3:59"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>and </b><br/><a NAME="E4:59"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_4.html#R2" target="_self">is_coplanar</a> 
 <b>and </b><br/><a NAME="E5:59"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#R2" target="_self">is_coplanar</a> 
 <b>and </b><br/><a NAME="E6:59"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:59"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>and </b><br/><a NAME="E9:59"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E10:59"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a> 
 <b>by </b><i><a class="txt" href="aff_4.html#E4:59"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_4.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E11:59"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a>  )
 
<b>by </b><i><a class="txt" href="aff_4.html#E5:59"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_4.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E12:59"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:59"><i><font color="Green">E48</font></i></a>, <a class="txt" href="aff_4.html#E6:59"><i><font color="Green">E51</font></i></a>, <a class="txt" href="aff_4.html#E8:59"><i><font color="Green">E52</font></i></a>, <a class="txt" href="aff_4.html#E10:59"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_4.html#T26" target="_self">Th26</a></i>;<br/>
<b>hence </b><a NAME="E13:59"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="aff_4.html#R2" target="_self">is_coplanar</a> 
 <b>by </b><i><a class="txt" href="aff_4.html#E8:59"><i><font color="Green">E52</font></i></a>, <a class="txt" href="aff_4.html#E9:59"><i><font color="Green">E53</font></i></a>, <a class="txt" href="aff_4.html#E10:59"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_4.html#D5" target="_self">Def5</a></i>;<br/>


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