<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="translac.html#NR1" target="_self">satisfies_Fano</a>  )
 <b>and </b><br/><a NAME="E2:28"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 <b>and </b><br/><a NAME="E4:28"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 <b>and </b><br/><a NAME="E5:28"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:28"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E7:28"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a>  <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 
<b>by </b><i><a class="txt" href="translac.html#E4:28"><i><font color="Green">E27</font></i></a>, <a class="ref" href="transgeo.html#T104">TRANSGEO:104</a></i>;<br/>
<a NAME="E8:28"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#NR9" target="_self">is_Tr</a> 
 
<b>by </b><i><a class="txt" href="translac.html#E3:28"><i><font color="Green">E26</font></i></a>, <a class="ref" href="transgeo.html#T105">TRANSGEO:105</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="transgeo.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="translac.html#E1:28"><i><font color="Green">E25</font></i></a>, <a class="txt" href="translac.html#E3:28"><i><font color="Green">E26</font></i></a>, <a class="txt" href="translac.html#E7:28"><i><font color="Green">E30</font></i></a>, <a class="ref" href="translac.html#T12" target="_self">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span> <a href="transgeo.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="translac.html#E5:28"><i><font color="Green">E28</font></i></a>, <a class="txt" href="translac.html#E6:28"><i><font color="Green">E29</font></i></a>, <a class="ref" href="funct_1.html#T66">FUNCT_1:66</a></i>
<br/>.= 
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="funct_2.html#T88">FUNCT_2:88</a></i>
;<br/>
<a NAME="E10:28"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:28"><i><font color="Green">E25</font></i></a>, <a class="txt" href="translac.html#E8:28"><i><font color="Green">E31</font></i></a>, <a class="ref" href="translac.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E11:28"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="transgeo.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T88">FUNCT_2:88</a></i>;<br/>
<b>hence </b><a NAME="E12:28"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="transgeo.html#T13">TRANSGEO:13</a></i>;<br/>


</div>
