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<b>let </b><font color="Maroon">OAS</font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">OAS</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:63"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 <b>and </b><br/><a NAME="E2:63"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>and </b><br/><a NAME="E3:63"/><i><font color="Green">E26</font></i>: 
not  <a href="diraf.html#R3">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font>
 ;<br/>

<b>assume </b><a NAME="E4:63"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E5:63"/>
<font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:63"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5">DIRAF:def 5</a></i>;<br/>
<a NAME="E7:63"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T36">DIRAF:36</a></i>;<br/>
<a NAME="E8:63"/>
<font color="Maroon">b</font>,<font color="Maroon">x</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E9:63"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5">DIRAF:def 5</a></i>;<br/>
<a NAME="E10:63"/><b>then </b>
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>,<font color="Maroon">x</font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>,<font color="Maroon">b</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T36">DIRAF:36</a>, <a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/>
<b>hence </b><a NAME="E11:63"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E13"><i><font color="Green">Lemma38</font></i></a>, <a class="txt" href="transgeo.html#E14"><i><font color="Green">Lemma39</font></i></a>, , <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/>


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