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<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">a</font>, <font color="Maroon" title="c3">b</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="c4">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="E1:75"/><i><font color="Green" title="E45">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="transgeo.html#NR7" title="TRANSGEO:NR.7">is_Tr</a> 
 <b>and </b><br/><a NAME="E2:75"/><i><font color="Green" title="E46">A2</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>and </b><br/><a NAME="E3:75"/><i><font color="Green" title="E47">A3</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 ;<br/>

<a NAME="E4:75"/><i><font color="Green" title="E48">A4</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:75"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="transgeo.html#E2:75"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="transgeo.html#E3:75"><i><font color="Green" title="E47">A3</font></i></a>, <a class="txt" href="transgeo.html#E87"><i><font color="Green" title="E43">Lm6</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:75_1"/><i><font color="Green" title="E49">A5</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 ;<br/><a NAME="E2:75_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:75"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></i>;<br/><a NAME="E3:75_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E4:75_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E5:75_1"/><b>then </b><i><font color="Green" title="E50">A6</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/><a NAME="E6:75_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:75"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E7:75_1"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E3:75"><i><font color="Green" title="E47">A3</font></i></a>, <a class="txt" href="transgeo.html#E4:75"><i><font color="Green" title="E48">A4</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E8:75_1"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><b>hence </b><a NAME="E9:75_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:75_1"><i><font color="Green" title="E49">A5</font></i></a>, <a class="txt" href="transgeo.html#E5:75_1"><i><font color="Green" title="E50">A6</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:75"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:75"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="transgeo.html#E2:75"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="transgeo.html#E3:75"><i><font color="Green" title="E47">A3</font></i></a>, <a class="txt" href="transgeo.html#E87"><i><font color="Green" title="E43">Lm6</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>


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