<?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>thus </b><a NAME="E1:11"/>
( <font color="Maroon">AFP</font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a>  implies for <font color="Olive">a</font>, <font color="Olive">a'</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">b'</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>  st not  <a href="aff_1.html#R1">LIN</a> <font color="Olive">a</font>,<font color="Olive">a'</font>,<font color="Olive">b</font> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Olive">a</font>,<font color="Olive">a'</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c'</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">AFP</font> <a href="aff_2.html#NR11" target="_self">satisfies_des</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">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="E2:11_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>set </b><font color="Maroon">A</font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>;<br/>
<b>set </b><font color="Maroon">P</font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font>;<br/>
<b>set </b><font color="Maroon">C</font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font>;<br/>
<a NAME="E3:11_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E4:11_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font>
 ;<br/>

<a NAME="E2:11_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:11_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:11_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:11_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font>
 ;<br/>

<a NAME="E2:11_1_2"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:11_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:11_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:11_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">b'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font> &amp; <font color="Maroon">c'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T26">AFF_1:26</a></i>;<br/>
<a NAME="E7:11_1"/><i><font color="Green">E31</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<a NAME="E8:11_1"/><i><font color="Green">E32</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp;  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="aff_1.html#R4">//</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font> )
 
<b>by </b><i>, , , , <a class="ref" href="aff_1.html#T51">AFF_1:51</a></i>;<br/>
<a NAME="E9:11_1"/><i><font color="Green">E33</font></i>: 
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E10:11_1"/>
 <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E11:11_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="ref" href="aff_2.html#D11">AFF_2:def 11</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:11"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">a'</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">b'</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFP</font>  st not  <a href="aff_1.html#R1">LIN</a> <font color="Olive">a</font>,<font color="Olive">a'</font>,<font color="Olive">b</font> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Olive">a</font>,<font color="Olive">a'</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c'</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AFP</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</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">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>assume </b><a NAME="E1:11_2"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">P</font> &amp; <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">b'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">c'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">P</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">C</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">P</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <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/><a NAME="E2:11_2"/><b>then </b><i><font color="Green">E36</font></i>: 
( <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> )
 <b>by </b><i><a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><div><i><font color="Green">E37</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font>
 ;<br/><a NAME="E2:11_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">b'</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E3:11_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E4:11_2_1"/><b>then </b><i><font color="Green">E41</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E5:11_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">c'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E6:11_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E7:11_2_1"/><b>then </b>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E8:11_2_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="ref" href="aff_1.html#T11">AFF_1:11</a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a'</font>
 ;<br/><a NAME="E2:11_2_2"/><i><font color="Green">E44</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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_2_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:11_2_2_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E3:11_2_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:11_2_2"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>,<font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_2_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>,<font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:11_2_2_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E3:11_2_2_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:11_2_2"/>
<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>, , , </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:11_2"/>
<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/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:11"/>
<font color="Maroon">AFP</font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a> 
 <b>by </b><i><a class="ref" href="aff_2.html#D11">AFF_2:def 11</a></i>;<br/>


</div>
