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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>thus </b><a NAME="E1:90"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR8" target="_self">is_Dil</a>  implies for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></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">c<sub>2</sub></font> <a href="transgeo.html#NR8" target="_self">is_Dil</a> 
 ;<br/>

<a NAME="E2:90_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#R3" target="_self">is_DIL_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="transgeo.html#D10" target="_self">Def10</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>thus </b><a NAME="E3:90_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:90_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="transgeo.html#T35" target="_self">Th35</a></i>;<br/>


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

<b>assume </b><a NAME="E2:90"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/>

<a NAME="E3:90"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#R3" target="_self">is_DIL_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="transgeo.html#T35" target="_self">Th35</a></i>;<br/>
<b>hence </b><a NAME="E4:90"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR8" target="_self">is_Dil</a> 
 <b>by </b><i><a class="ref" href="transgeo.html#D10" target="_self">Def10</a></i>;<br/>


</div>
