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<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">A</font> <a href="aff_1.html#R4" target="_self">//</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">C</font> <a href="aff_1.html#R4" target="_self">//</a> <font color="Maroon">D</font>
 ;<br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E4:57"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> )
 <b>by </b><i><a class="txt" href="aff_1.html#E5:57"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E5:57"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">C</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">D</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>then consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E7:57"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> )
 <b>by </b><i/>;<br/>
<a NAME="E8:57"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:57"/>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="txt" href="aff_1.html#E7:57"><i><font color="Green">E52</font></i></a>, </i>;<br/>
<a NAME="E10:57"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 
<b>by </b><i>, <a class="txt" href="aff_1.html#E7:57"><i><font color="Green">E52</font></i></a>, , , , <a class="ref" href="aff_1.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E11:57"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> )
 
<b>by </b><i><a class="txt" href="aff_1.html#E7:57"><i><font color="Green">E52</font></i></a>, , </i>;<br/>
<b>hence </b><a NAME="E12:57"/>
<font color="Maroon">A</font> <a href="aff_1.html#R4" target="_self">//</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T20" target="_self">Th20</a></i>;<br/>


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