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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">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/>





<b>assume </b><a NAME="E1:32"/>
<font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 ;<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="E3:32"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> )
 <b>by </b><i><a class="txt" href="aff_1.html#E3:32"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E4:32"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> implies ( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> ) )
 
<b>by </b><i><a class="txt" href="aff_1.html#E13"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:32"/>
 ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="txt" href="aff_1.html#E13"><i><font color="Green">Lemma29</font></i></a></i>;<br/>


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