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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>given </b><font color="Maroon" title="c2">f</font> being   <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><b> such that </b><a NAME="E1:46"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR5" title="TRANSGEO:NR.5">is_SDil</a>  &amp; <font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR4" title="TRANSGEO:NR.4">is_CDil</a>  )
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E3:46"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="realset2.html#D7" title="REALSET2:def.7">REALSET2:def 7</a></i>;<br/>
<a NAME="E4:46"/>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:46"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="transgeo.html#D7" target="_self" title="TRANSGEO:def.7">Def7</a>, <a class="ref" href="transgeo.html#T42" target="_self" title="TRANSGEO:th.42">Th42</a></i>;<br/>
<a NAME="E5:46"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E3:46"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E6:46"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">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="E7:46"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E3:46"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="funct_2.html#T85" title="FUNCT_2:th.85">FUNCT_2:85</a></i>;<br/>


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