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

<b>let </b><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">OAS</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:79"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="transgeo.html#NR6" title="TRANSGEO:NR.6">is_Dil</a> 
 <b>and </b><br/><a NAME="E2:79"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E3:79"/><i><font color="Green" title="E51">A3</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font>
 <b>and </b><br/><a NAME="E4:79"/><i><font color="Green" title="E52">A4</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">x</font>
 ;<br/>

<a NAME="E5:79"/>
<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:79"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="transgeo.html#E2:79"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/>
<a NAME="E6:79"/><b>then </b><i><font color="Green" title="E53">A5</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>
<a NAME="E7:79"/>
<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:79"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/>
<a NAME="E8:79"/><b>then </b>
<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">q</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>
<b>hence </b><a NAME="E9:79"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E3:79"><i><font color="Green" title="E51">A3</font></i></a>, <a class="txt" href="transgeo.html#E4:79"><i><font color="Green" title="E52">A4</font></i></a>, <a class="txt" href="transgeo.html#E6:79"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="pasch.html#T13" title="PASCH:th.13">PASCH:13</a></i>;<br/>


</div>
