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<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="E1:90"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</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> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="euclidlp.html#R6" target="_self">_|_</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E2:90"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="euclidlp.html#T80" target="_self">Th80</a></i>;<br/>
<a NAME="E3:90"/><i><font color="Green">E82</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="txt" href="euclidlp.html#E1:90"><i><font color="Green">E80</font></i></a>, <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="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="E5:90"/><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E2:90"><i><font color="Green">E81</font></i></a>, <a class="txt" href="euclidlp.html#E3:90"><i><font color="Green">E82</font></i></a>, <a class="ref" href="euclidlp.html#T84" target="_self">Th84</a></i>;<br/>
<b>thus </b><a NAME="E6:90"/>
ex <font color="Olive">b<sub>1</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> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E1:90"><i><font color="Green">E80</font></i></a>, <a class="txt" href="euclidlp.html#E5:90"><i><font color="Green">E83</font></i></a></i>;<br/>


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