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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="euclidlp.html#K1" title="EUCLIDLP:func.1">line_of_REAL</a> <font color="Maroon" title="c1">n</font>;<br/>







<b>assume </b><a NAME="E1:90"/><i><font color="Green" title="E80">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">L1</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> &amp; <font color="Maroon" title="c3">L1</font> <a href="euclidlp.html#R6" title="EUCLIDLP:pred.6">_|_</a> <font color="Maroon" title="c4">L2</font> )
 ;<br/>

<a NAME="E2:90"/><b>then </b><i><font color="Green" title="E81">A2</font></i>: 
<font color="Maroon" title="c3">L1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">L2</font>
 
<b>by </b><i><a class="ref" href="euclidlp.html#T80" target="_self" title="EUCLIDLP:th.80">Th80</a></i>;<br/>
<a NAME="E3:90"/><i><font color="Green" title="E82">A3</font></i>: 
( <font color="Maroon" title="c3">L1</font> <a href="euclid_4.html#NR1" title="EUCLID_4:NR.1">is_line</a>  &amp; <font color="Maroon" title="c4">L2</font> <a href="euclid_4.html#NR1" title="EUCLID_4:NR.1">is_line</a>  )
 
<b>by </b><i><a class="txt" href="euclidlp.html#E1:90"><i><font color="Green" title="E80">A1</font></i></a>, <a class="ref" href="euclidlp.html#T72" target="_self" title="EUCLIDLP:th.72">Th72</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">x0</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E5:90"/><i><font color="Green" title="E83">A4</font></i>: 
( <font color="Maroon" title="c5">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">L1</font> &amp; not <font color="Maroon" title="c5">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E2:90"><i><font color="Green" title="E81">A2</font></i></a>, <a class="txt" href="euclidlp.html#E3:90"><i><font color="Green" title="E82">A3</font></i></a>, <a class="ref" href="euclidlp.html#T84" target="_self" title="EUCLIDLP:th.84">Th84</a></i>;<br/>
<b>thus </b><a NAME="E6:90"/>
 ex <font color="Olive" title="b1">x0</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x0</font> &amp; <font color="Olive" title="b1">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">L1</font> &amp; not <font color="Olive" title="b1">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">L2</font> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E1:90"><i><font color="Green" title="E80">A1</font></i></a>, <a class="txt" href="euclidlp.html#E5:90"><i><font color="Green" title="E83">A4</font></i></a></i>;<br/>


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