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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/>



<div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 ;<br/><a NAME="E2:51_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#R1" target="_self">is_FormalIz_of</a>  <a href="diraf.html#K1">lambda</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="transgeo.html#D8" target="_self">Def8</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/><a NAME="E3:51_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="diraf.html#K1">lambda</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:51_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="transgeo.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E4:51_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.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="ref" href="diraf.html#T23">DIRAF:23</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_2"/><i><font color="Green">E29</font></i>: 
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="diraf.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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2_1"><b>now </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="E1:51_2_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.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#E1:51_2"><i><font color="Green">E29</font></i></a></i>;<br/><b>hence </b><a NAME="E2:51_2_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="diraf.html#K1">lambda</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T23">DIRAF:23</a></i>;<br/></div><b>end;</b></div><a NAME="E3:51_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#R1" target="_self">is_FormalIz_of</a>  <a href="diraf.html#K1">lambda</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="transgeo.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E4:51_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR6" target="_self">is_Dil</a> 
 <b>by </b><i><a class="ref" href="transgeo.html#D8" target="_self">Def8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:51"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#NR6" target="_self">is_Dil</a>  iff 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="diraf.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> )
 <b>by </b><i><a class="txt" href="transgeo.html#E1:51"><i><font color="Green">E28</font></i></a></i>;<br/>


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