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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">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/>





<b>assume </b><a NAME="E1:18"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/>

<b>assume </b><a NAME="E2:18"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> holds   <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Olive">z</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><b> such that </b><br/><a NAME="E4:18"/><i><font color="Green">E40</font></i>: 
not  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:18"/>
(  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">a</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">b</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:18"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


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