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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:89"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="euclidlp.html#R6" target="_self">_|_</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:89"/><b>then </b><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  )
 
<b>by </b><i><a class="ref" href="euclidlp.html#T72" target="_self">Th72</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="euclidlp.html#K1" target="_self">line_of_REAL</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:89"/><i><font color="Green">E81</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="euclidlp.html#R5" target="_self">//</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E2:89"><i><font color="Green">E80</font></i></a>, <a class="ref" href="euclidlp.html#T77" target="_self">Th77</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E5:89"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="euclidlp.html#R6" target="_self">_|_</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="euclidlp.html#R5" target="_self">//</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E1:89"><i><font color="Green">E79</font></i></a>, <a class="txt" href="euclidlp.html#E4:89"><i><font color="Green">E81</font></i></a>, <a class="ref" href="euclidlp.html#T66" target="_self">Th66</a></i>;<br/>


</div>
