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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">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>let </b><font color="Maroon">g</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="E1:69"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">f</font> <a href="transgeo.html#NR7" target="_self">is_Tr</a>  &amp; <font color="Maroon">g</font> <a href="transgeo.html#NR7" target="_self">is_Tr</a>  )
 <b>and </b><br/><a NAME="E2:69"/><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">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E3:69"/><i><font color="Green">E26</font></i>: 
not  <a href="diraf.html#R3">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>,<font color="Maroon">x</font>
 ;<br/>

<a NAME="E4:69"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">f</font> <a href="transgeo.html#NR6" target="_self">is_Dil</a>  &amp; <font color="Maroon">g</font> <a href="transgeo.html#NR6" target="_self">is_Dil</a>  )
 
<b>by </b><i>, </i>;<br/>
<b>set </b><font color="Maroon">b</font> = <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>;<br/>
<b>set </b><font color="Maroon">y</font> = <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>;<br/>
<b>set </b><font color="Maroon">z</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>;<br/>
<a NAME="E5:69"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="diraf.html#R2">'||'</a> <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="transgeo.html#T24" target="_self">Th24</a>, , <a class="txt" href="transgeo.html#E13"><i><font color="Green">Lemma38</font></i></a></i>;<br/>
<a NAME="E6:69"/>
( <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>,<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, <a class="ref" href="transgeo.html#D2" target="_self">Def2</a>, <a class="ref" href="transgeo.html#T24" target="_self">Th24</a>, , <a class="txt" href="transgeo.html#E13"><i><font color="Green">Lemma38</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:69"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="transgeo.html#T23" target="_self">Th23</a>, <a class="ref" href="transgeo.html#T26" target="_self">Th26</a>, <a class="ref" href="pasch.html#T12">PASCH:12</a></i>;<br/>


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