<?xml version="1.0"?>
<div class="add">

<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> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</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="E1:26"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a> 
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green">E23</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>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E4:26"/><i><font color="Green">E24</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:26"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<a NAME="E5:26"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T26">AFF_1:26</a></i>;<br/>
<a NAME="E6:26"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; not <font color="Olive">b<sub>1</sub></font> <a href="aff_1.html#R4">//</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_4.html#K1" target="_self">Plane</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:26"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_4.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:26"><i><font color="Green">E22</font></i></a>, <a class="txt" href="aff_4.html#E3:26"><i><font color="Green">E23</font></i></a>, <a class="txt" href="aff_4.html#E4:26"><i><font color="Green">E24</font></i></a>, <a class="txt" href="aff_4.html#E5:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="aff_4.html#E25"><i><font color="Green">Lemma19</font></i></a></i>;<br/>


</div>
