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<b>let </b><font color="Maroon">AFP</font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/>

<b>assume </b><a NAME="E1:22"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>  ex <font color="Olive">f</font> being  <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFP</font> st <br/>( <font color="Olive">f</font> <a href="transgeo.html#NR9" target="_self">is_Tr</a>  &amp; <font color="Olive">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">c'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/><b>assume </b><a NAME="E1:22_1"/><i><font color="Green">E24</font></i>: 
( not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>,<font color="Maroon">b</font> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font> )
 ;<br/><b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFP</font><b> such that </b><br/><a NAME="E3:22_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 <b>and </b><br/><a NAME="E4:22_1"/><i><font color="Green">E26</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">a'</font>
 <b>by </b><i><a class="ref" href="translac.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E5:22_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">b'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="translac.html#E2"><i><font color="Green">Lemma22</font></i></a>, <a class="txt" href="translac.html#E1:22"><i><font color="Green">E23</font></i></a>, <a class="txt" href="translac.html#E1:22_1"><i><font color="Green">E24</font></i></a>, </i>;<br/><a NAME="E6:22_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="translac.html#E2"><i><font color="Green">Lemma22</font></i></a>, <a class="txt" href="translac.html#E1:22"><i><font color="Green">E23</font></i></a>, <a class="txt" href="translac.html#E1:22_1"><i><font color="Green">E24</font></i></a>, </i>;<br/><a NAME="E7:22_1"/>
<font color="Maroon">f</font> <a href="transgeo.html#NR8" target="_self">is_Dil</a> 
 <b>by </b><i><a class="txt" href="translac.html#E1:22"><i><font color="Green">E23</font></i></a>, <a class="ref" href="transgeo.html#D11">TRANSGEO:def 11</a></i>;<br/><b>hence </b><a NAME="E8:22_1"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 <b>by </b><i><a class="txt" href="translac.html#E3:22_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="translac.html#E4:22_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="transgeo.html#T85">TRANSGEO:85</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:22"/>
<font color="Maroon">AFP</font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a> 
 <b>by </b><i/>;<br/>


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