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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#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<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>assume </b><a NAME="E1:47"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2" target="_self">//</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i><a class="txt" href="aff_1.html#E19"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<a NAME="E3:47"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2" target="_self">//</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T19" target="_self">Th19</a>, <a class="ref" href="aff_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
contradiction
 <b>by </b><i><a class="ref" href="aff_1.html#T19" target="_self">Th19</a>, <a class="ref" href="aff_1.html#T20" target="_self">Th20</a>, <a class="ref" href="aff_1.html#T13" target="_self">Th13</a></i>;<br/>


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