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

<b>let </b><font color="Maroon">AFP</font> be   <a href="diraf.html#NM2">AffinPlane</a>;<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">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AFP</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">AFP</font>;<br/>









<b>assume </b><a NAME="E1:32"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 ;<br/>

<b>assume </b><a NAME="E2:32"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font> holds <br/> ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> iff ( ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> ) or ( not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp;  ex <font color="Olive">p</font>, <font color="Olive">p'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Olive">p'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Olive">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p'</font>,<font color="Olive">x</font> &amp; <font color="Olive">p</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p'</font>,<font color="Olive">y</font> &amp; <font color="Olive">x</font>,<font color="Olive">y</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">K</font> ) ) ) )
 ;<br/>

<a NAME="E3:32"/>
<font color="Maroon">K</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T40">AFF_1:40</a></i>;<br/>
<b>then consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>, <font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font><b> such that </b><br/><a NAME="E5:32"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</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="aff_1.html#T31">AFF_1:31</a></i>;<br/>
<a NAME="E6:32"/>
( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">b</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<b>hence </b><a NAME="E7:32"/>
<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">b</font>
 <b>by </b><i>, , </i>;<br/>


</div>
