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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="analoaf.html#NM1">OAffinSpace</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>assume </b><a NAME="E1:78"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR7" target="_self">is_Tr</a> 
 ;<br/>

<a NAME="E2:78"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR4" target="_self">is_CDil</a>  )
 
<b>by </b><i><a class="ref" href="transgeo.html#T44" target="_self">Th44</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:78_1"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/><a NAME="E2:78_1"/>
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="78_1_1"><b>proof </b></a><div class="add">

<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/>



<a NAME="E1:78_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:78_1"><i><font color="Green">E50</font></i></a></i>;<br/>
<a NAME="E2:78_1_1"/>
( not  <a href="diraf.html#R3">LIN</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> implies <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#E1:78"><i><font color="Green">E48</font></i></a>, <a class="txt" href="transgeo.html#E86"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:78_1_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#E1:78"><i><font color="Green">E48</font></i></a>, <a class="txt" href="transgeo.html#E1:78_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="transgeo.html#E90"><i><font color="Green">Lemma46</font></i></a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:78_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR4" target="_self">is_CDil</a> 
 <b>by </b><i><a class="ref" href="transgeo.html#T42" target="_self">Th42</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:78"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR4" target="_self">is_CDil</a> 
 <b>by </b><i><a class="txt" href="transgeo.html#E1:78"><i><font color="Green">E48</font></i></a>, <a class="txt" href="transgeo.html#E2:78"><i><font color="Green">E49</font></i></a>, <a class="ref" href="transgeo.html#D9" target="_self">Def9</a></i>;<br/>


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