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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">L1</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>let </b><font color="Maroon">L2</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="E1:117"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">L1</font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  &amp; <font color="Maroon">L2</font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  &amp; <font color="Maroon">L1</font>,<font color="Maroon">L2</font> <a href="euclidlp.html#R7" target="_self">are_coplane</a>  &amp; <font color="Maroon">L1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">L2</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">P</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">n</font><b> such that </b><br/><a NAME="E3:117"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">L1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> &amp; <font color="Maroon">L2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">x</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="E5:117"/><i><font color="Green">E88</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L2</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L1</font> )
 <b>by </b><i><a class="ref" href="euclidlp.html#D2" target="_self">Def2</a>, <a class="ref" href="euclidlp.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E6:117"/>
<font color="Maroon">P</font> is <a href="euclidlp.html#V1" target="_self">being_plane</a>
 
<b>by </b><i><a class="ref" href="euclidlp.html#D2" target="_self">Def2</a>, <a class="txt" href="euclidlp.html#E43"><i><font color="Green">Lemma98</font></i></a>, <a class="ref" href="euclidlp.html#T40" target="_self">Th40</a>, <a class="ref" href="euclidlp.html#T37" target="_self">Th37</a></i>;<br/>
<b>hence </b><a NAME="E7:117"/>
 ex <font color="Olive">P</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">n</font> st <br/>( <font color="Maroon">L1</font> <a href="tarski.html#R1">c=</a> <font color="Olive">P</font> &amp; <font color="Maroon">L2</font> <a href="tarski.html#R1">c=</a> <font color="Olive">P</font> &amp; <font color="Olive">P</font> is <a href="euclidlp.html#V1" target="_self">being_plane</a> )
 <b>by </b><i><a class="txt" href="euclidlp.html#E43"><i><font color="Green">Lemma98</font></i></a></i>;<br/>


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