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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">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="E1:65"/><i><font color="Green">E22</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>and </b><br/><a NAME="E2:65"/><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> &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">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> )
 ;<br/>

<b>assume </b><a NAME="E3:65"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<i><font color="Green">E28</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="txt" href="transgeo.html#E13"><i><font color="Green">Lemma38</font></i></a>, <a class="ref" href="funct_2.html#T70">FUNCT_2:70</a></i>
<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i/>
;<br/>
<i><font color="Green">E30</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="txt" href="transgeo.html#E13"><i><font color="Green">Lemma38</font></i></a>, <a class="ref" href="funct_2.html#T70">FUNCT_2:70</a></i>
<br/>.= 
<font color="Maroon">b</font>
<b>by </b><i/>
;<br/>
<a NAME="E6:65"/>
<font color="Maroon">g</font> <a href="funct_2.html#K2">"</a>  <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 
<b>by </b><i>, <a class="txt" href="transgeo.html#E4:65"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E7:65"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">f</font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:65"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1" target="_self">*</a> <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">OAS</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E14"><i><font color="Green">Lemma39</font></i></a>, , <a class="ref" href="transgeo.html#D2" target="_self">Def2</a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><a NAME="E1:65_3"/>
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T70">FUNCT_2:70</a></i>;<br/><a NAME="E2:65_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</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="funct_1.html#T35">FUNCT_1:35</a></i>;<br/><b>hence </b><a NAME="E3:65_3"/>
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:65"/>
<font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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