<?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>, <font color="Maroon">c<sub>3</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="E1:118"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  &amp; <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>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> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:118"/><i><font color="Green">E98</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T84" target="_self">Th84</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#K5" target="_self">plane_of_REAL</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:118"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="euclidlp.html#V1" target="_self">being_plane</a> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E1:118"><i><font color="Green">E97</font></i></a>, <a class="txt" href="euclidlp.html#E3:118"><i><font color="Green">E98</font></i></a>, <a class="ref" href="euclidlp.html#T105" target="_self">Th105</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:118"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E1:118"><i><font color="Green">E97</font></i></a>, <a class="ref" href="euclidlp.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E8:118"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K2">Line</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="euclidlp.html#E7:118"><i><font color="Green">E100</font></i></a>, <a class="txt" href="euclidlp.html#E3:118"><i><font color="Green">E98</font></i></a>, <a class="txt" href="euclidlp.html#E1:118"><i><font color="Green">E97</font></i></a>, <a class="ref" href="euclidlp.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E9:118"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="euclidlp.html#E5:118"><i><font color="Green">E99</font></i></a>, <a class="txt" href="euclidlp.html#E7:118"><i><font color="Green">E100</font></i></a>, <a class="ref" href="euclidlp.html#T100" target="_self">Th100</a></i>;<br/>
<b>hence </b><a NAME="E10:118"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="euclidlp.html#K5" target="_self">plane_of_REAL</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <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="Maroon">c<sub>3</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> is <a href="euclidlp.html#V1" target="_self">being_plane</a> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E5:118"><i><font color="Green">E99</font></i></a></i>;<br/>


</div>
