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









<b>assume </b><a NAME="E1:59"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2" target="_self">//</a> <font color="Maroon">K</font> )
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:59"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 <b>and </b><br/><a NAME="E3:59"/><i><font color="Green">E40</font></i>: 
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<b>set </b><font color="Maroon">A</font> =  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>
<a NAME="E4:59"/>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:59"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:59"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:59"/>
 <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R4" target="_self">//</a> <font color="Maroon">K</font>
 
<b>by </b><i>, <a class="txt" href="aff_1.html#E6:59"><i><font color="Green">E52</font></i></a>, <a class="txt" href="aff_1.html#E15"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:59"/>
contradiction
 <b>by </b><i>, , , <a class="txt" href="aff_1.html#E5:59"><i><font color="Green">E50</font></i></a></i>;<br/>


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