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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">A</font> be   <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>, <font color="Maroon">C</font> be   <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>;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">A</font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  &amp; <font color="Maroon">C</font> <a href="euclid_4.html#NR1" target="_self">is_line</a>  &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>

<b>assume </b><a NAME="E2:21"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x2</font>
 ;<br/>

<a NAME="E3:21"/><b>then </b>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:21"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/>


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