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

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="euclidlp.html#K1" target="_self">line_of_REAL</a> <font color="Maroon">n</font>;<br/>





<a NAME="E1:113"/>
<font color="Maroon">L</font> <a href="hidden.html#R2">in</a>  <a href="euclidlp.html#K1" target="_self">line_of_REAL</a> <font color="Maroon">n</font>
 
;<br/>
<b>then consider </b><font color="Maroon">L0</font> being   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font></span>)</span><b> such that </b><br/><a NAME="E3:113"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L0</font> &amp;  ex <font color="Olive">x1</font>, <font color="Olive">x2</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> st <font color="Maroon">L0</font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K2">Line</a> <font color="Olive">x1</font>,<font color="Olive">x2</font> )
 ;<br/>
<b>consider </b><font color="Maroon">x1</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">x2</font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E5:113"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K2">Line</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font>
 <b>by </b><i><a class="ref" href="euclidlp.html#D1" target="_self">Def1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">P</font> =  <a href="euclidlp.html#K4" target="_self">plane</a> <font color="Maroon">x</font>,<font color="Maroon">x1</font>,<font color="Maroon">x2</font> as   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font></span>)</span> ;<br/>
<a NAME="E7:113"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 
<b>by </b><i><a class="ref" href="euclidlp.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E8:113"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="euclidlp.html#T37" target="_self">Th37</a>, <a class="ref" href="euclidlp.html#T29" target="_self">Th29</a></i>;<br/>
<b>take </b>
<font color="Maroon">P</font>
;<br/>

<b>thus </b><a NAME="E9:113"/>
( <font color="Maroon">P</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="euclidlp.html#K5" target="_self">plane_of_REAL</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T31" target="_self">Th31</a>, <a class="ref" href="euclidlp.html#T27" target="_self">Th27</a>, <a class="ref" href="euclidlp.html#T38" target="_self">Th38</a></i>;<br/>


</div>
