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<div class="add">

<b>let </b><font color="Maroon" title="c1">AFS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">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">AFS</font>;<br/>



<b>thus </b><a NAME="E1:90"/>
( <font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR8" title="TRANSGEO:NR.8">is_Dil</a>  implies for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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="Olive" title="b1">a</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:90_1"/>
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR8" title="TRANSGEO:NR.8">is_Dil</a> 
 ;<br/>

<a NAME="E2:90_1"/><b>then </b><i><font color="Green" title="E57">A1</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a> <font color="Maroon" title="c1">AFS</font>
 
<b>by </b><i><a class="ref" href="transgeo.html#D10" target="_self" title="TRANSGEO:def.10">Def10</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFS</font>;<br/>



<b>thus </b><a NAME="E3:90_1"/>
<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>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:90_1"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="transgeo.html#T35" target="_self" title="TRANSGEO:th.35">Th35</a></i>;<br/>


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

<b>assume </b><a NAME="E2:90"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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="Olive" title="b1">a</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font>
 ;<br/>

<a NAME="E3:90"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a> <font color="Maroon" title="c1">AFS</font>
 
<b>by </b><i><a class="ref" href="transgeo.html#T35" target="_self" title="TRANSGEO:th.35">Th35</a></i>;<br/>
<b>hence </b><a NAME="E4:90"/>
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR8" title="TRANSGEO:NR.8">is_Dil</a> 
 <b>by </b><i><a class="ref" href="transgeo.html#D10" target="_self" title="TRANSGEO:def.10">Def10</a></i>;<br/>


</div>
