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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">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/>





<b>assume </b><a NAME="E1:82"/><i><font color="Green">E59</font></i>: 
( not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> &amp; <font color="Maroon">L</font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  )
 ;<br/>

<b>consider </b><font color="Maroon">L0</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">n</font><b> such that </b><br/><a NAME="E3:82"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L0</font> &amp; <font color="Maroon">L0</font> <a href="euclidlp.html#R5" target="_self">//</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T17" target="_self">Th17</a>, <a class="ref" href="euclidlp.html#T16" target="_self">Th16</a></i>;<br/>
<b>thus </b><a NAME="E4:82"/>
 ex <font color="Olive">L0</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">n</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">L0</font> &amp; <font color="Olive">L0</font> <a href="euclidlp.html#R5" target="_self">//</a> <font color="Maroon">L</font> &amp; <font color="Olive">L0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#T17" target="_self">Th17</a>, <a class="ref" href="euclidlp.html#T18" target="_self">Th18</a></i>;<br/>


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