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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">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>assume </b><a NAME="E1:106"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR8" target="_self">is_Dil</a> 
 ;<br/>

<a NAME="E2:106"/><b>then </b>
( ( <font color="Maroon">f</font> <a href="funct_2.html#R2">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFS</font> or for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font>  holds <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">x</font> ) iff for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font> holds  <font color="Olive">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="analoaf.html#R2">//</a> <font color="Olive">y</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E44"><i><font color="Green">Lemma63</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:106"/>
( <font color="Maroon">f</font> <a href="transgeo.html#NR9" target="_self">is_Tr</a>  iff for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font> holds  <font color="Olive">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="analoaf.html#R2">//</a> <font color="Olive">y</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> )
 <b>by </b><i>, <a class="ref" href="transgeo.html#T38" target="_self">Th38</a></i>;<br/>


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