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<b>let </b><font color="Maroon">OAS</font> be   <a href="analoaf.html#NM1">OAffinSpace</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">OAS</font>;<br/>



<b>assume </b><a NAME="E1:58"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/>







<a NAME="E2:58"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.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>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:58"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
 
<b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<br/><a NAME="E2:58_1"/><b>then </b><i><font color="Green">E30</font></i>: 
( <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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="diraf.html#T28">DIRAF:28</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_1_1"/><i><font color="Green">E31</font></i>: 
<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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<br/><a NAME="E2:58_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> implies <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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T25">DIRAF:25</a></i>;<br/><b>hence </b><a NAME="E3:58_1_1"/>
<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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="diraf.html#T28">DIRAF:28</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:58_1"/>
<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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="diraf.html#T25">DIRAF:25</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_2"/><i><font color="Green">E34</font></i>: 
<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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
 ;<br/><div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_2_1"/>
<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">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E2:58_2_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T85">FUNCT_2:85</a></i>;<br/><b>hence </b><a NAME="E3:58_2_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="diraf.html#T25">DIRAF:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_2_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:58_2_2_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <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">d</font>
 ;<br/><a NAME="E2:58_2_2_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T85">FUNCT_2:85</a></i>;<br/><b>hence </b><a NAME="E3:58_2_2_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="diraf.html#T25">DIRAF:25</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:58_2_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i>, , <a class="ref" href="diraf.html#T28">DIRAF:28</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:58_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i>, <a class="txt" href="transgeo.html#E2:58_2"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="diraf.html#T28">DIRAF:28</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:58"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> iff <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> <a href="diraf.html#R2">'||'</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font> )
 <b>by </b><i/>;<br/>


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