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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">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><a NAME="E1:85"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 ;<br/>

<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:85_1"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</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>
 ;<br/><a NAME="E2:85_1"/><b>then </b>
<font color="Maroon">f</font> <a href="transgeo.html#NR7" target="_self">is_Tr</a> 
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:85_1"/>
<font color="Maroon">f</font> <a href="transgeo.html#NR4" target="_self">is_CDil</a> 
 <b>by </b><i><a class="ref" href="transgeo.html#T29" target="_self">Th29</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font><b> such that </b><a NAME="E1:85_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 ;<br/><div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="85_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:85_2_1"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font> holds  <font color="Maroon">p</font>,<font color="Olive">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>
 ;<br/><a NAME="E2:85_2_1"/><b>then </b>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font> holds  <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</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#D4" target="_self">Def4</a>, </i>;<br/><b>hence </b><a NAME="E3:85_2_1"/>
<font color="Maroon">f</font> <a href="transgeo.html#NR4" target="_self">is_CDil</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_2_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font><b> such that </b><a NAME="E1:85_2_2"/><i><font color="Green">E30</font></i>: 
not <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font>
 ;<br/><a NAME="E2:85_2_2"/>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font>
 <b>by </b><i>, <a class="ref" href="transgeo.html#D4" target="_self">Def4</a>, </i>;<br/><a NAME="E3:85_2_2"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font>,<font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="diraf.html#D4">DIRAF:def 4</a></i>;<br/><a NAME="E4:85_2_2"/><b>then </b>
<font color="Maroon">q</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5">DIRAF:5</a></i>;<br/><a NAME="E5:85_2_2"/><b>then </b>
(  <a href="diraf.html#R1">Mid</a> <font color="Maroon">q</font>,<font color="Maroon">p</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> )
 <b>by </b><i>, <a class="ref" href="diraf.html#D3">DIRAF:def 3</a></i>;<br/><b>hence </b><a NAME="E6:85_2_2"/>
<font color="Maroon">f</font> <a href="transgeo.html#NR5" target="_self">is_SDil</a> 
 <b>by </b><i>, <a class="ref" href="transgeo.html#D4" target="_self">Def4</a>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:85_2"/>
( <font color="Maroon">f</font> <a href="transgeo.html#NR4" target="_self">is_CDil</a>  or <font color="Maroon">f</font> <a href="transgeo.html#NR5" target="_self">is_SDil</a>  )
 <b>by </b><i><a class="ref" href="transgeo.html#T35" target="_self">Th35</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:85"/>
( <font color="Maroon">f</font> <a href="transgeo.html#NR4" target="_self">is_CDil</a>  or <font color="Maroon">f</font> <a href="transgeo.html#NR5" target="_self">is_SDil</a>  )
 <b>by </b><i/>;<br/>


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