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



<b>assume </b><b>that </b><br/><a NAME="E1:27"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">AFP</font> <a href="translac.html#NR1" target="_self">satisfies_Fano</a> 
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 <b>and </b><br/><a NAME="E3:27"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#K1">*</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">AFP</font>
 ;<br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>;<br/>
<b>assume </b><a NAME="E5:27"/>
<font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFP</font>
 ;<br/>

<a NAME="E6:27"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="txt" href="translac.html#E8:27"><i><font color="Green">E26</font></i></a>, <a class="ref" href="transgeo.html#D11">TRANSGEO:def 11</a></i>;<br/>
<b>then consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font><b> such that </b><br/><a NAME="E8:27"/><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">b</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T22">AFF_1:22</a></i>;<br/>
<a NAME="E9:27"/><i><font color="Green">E28</font></i>: 
<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#E8:27"><i><font color="Green">E26</font></i></a>, <a class="ref" href="transgeo.html#D11">TRANSGEO:def 11</a></i>;<br/>
<a NAME="E10:27"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">f</font> <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">b</font></span>)</span>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="transgeo.html#T85">TRANSGEO:85</a></i>;<br/>
<a NAME="E11:27"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="transgeo.html#K1">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T70">FUNCT_2:70</a></i>;<br/>
<a NAME="E12:27"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="txt" href="translac.html#E3"><i><font color="Green">Lemma27</font></i></a>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/>
<a NAME="E13:27"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">b</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">b</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">b</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</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">b</font> )
 
<b>by </b><i><a class="txt" href="translac.html#E8:27"><i><font color="Green">E26</font></i></a>, , <a class="ref" href="aff_1.html#T13">AFF_1:13</a>, <a class="ref" href="transgeo.html#T85">TRANSGEO:85</a>, <a class="ref" href="transgeo.html#T100">TRANSGEO:100</a></i>;<br/>
<b>hence </b><a NAME="E14:27"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E3:27"><i><font color="Green">E25</font></i></a>, <a class="txt" href="translac.html#E9:27"><i><font color="Green">E28</font></i></a>, </i>;<br/>


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