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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">q1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">p1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">p2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">q2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>









<b>consider </b><font color="Maroon">x1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">x2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E2:65"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> &amp;  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K7" target="_self">Line</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> )
 <b>by </b><i><a class="txt" href="euclid_4.html#E2:65"><i><font color="Green">E41</font></i></a></i>;<br/>
<b>assume </b><a NAME="E3:65"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K7" target="_self">Line</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> &amp; <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K7" target="_self">Line</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> &amp; <font color="Maroon">q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q2</font> )
 ;<br/>

<b>consider </b><font color="Maroon">y1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">y2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font><b> such that </b><br/><a NAME="E5:65"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> &amp; <font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q2</font> &amp;  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K7" target="_self">Line</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> )
 <b>by </b><i><a class="txt" href="euclid_4.html#E2:65"><i><font color="Green">E41</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:65"/>
 <a href="euclid_4.html#K7" target="_self">Line</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> <a href="tarski.html#R1">c=</a>  <a href="euclid_4.html#K7" target="_self">Line</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font>
 <b>by </b><i>, , <a class="ref" href="euclid_4.html#T7" target="_self">Th7</a>, </i>;<br/>


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