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<b>let </b><font color="Maroon">AFS</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">AFS</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</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">AFS</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">AFS</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:107"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">f</font> <a href="transgeo.html#NR9" target="_self">is_Tr</a>  &amp; <font color="Maroon">g</font> <a href="transgeo.html#NR9" target="_self">is_Tr</a>  )
 <b>and </b><br/><a NAME="E2:107"/><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="E3:107"/><i><font color="Green">E26</font></i>: 
not  <a href="aff_1.html#R1">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="E4:107"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">f</font> <a href="transgeo.html#NR8" target="_self">is_Dil</a>  &amp; <font color="Maroon">g</font> <a href="transgeo.html#NR8" target="_self">is_Dil</a>  )
 
<b>by </b><i>, <a class="ref" href="transgeo.html#T38" target="_self">Th38</a></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="E5:107"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="analoaf.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="analoaf.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#D4" target="_self">Def4</a>, <a class="ref" href="transgeo.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E6:107"/>
( <font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="analoaf.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="analoaf.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#D4" target="_self">Def4</a>, <a class="ref" href="transgeo.html#T39" target="_self">Th39</a></i>;<br/>
<b>hence </b><a NAME="E7:107"/>
<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#T37" target="_self">Th37</a></i>;<br/>


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