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<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">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="E1:57"/>
<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="E3:57"/><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="E5:57"/><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#T5" target="_self">Th5</a></i>;<br/>
<b>take </b>
<font color="Maroon">x1</font>
;<br/>

<b>take </b>
<font color="Maroon">x2</font>
;<br/>

<b>thus </b><a NAME="E6:57"/>
<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#T6" target="_self">Th6</a></i>;<br/>


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