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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>





<a NAME="E1:10"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">A</font> <a href="group_2.html#K1">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">g</font> <a href="group_1.html#K3">"</a> </span>)</span> where <font color="Olive">g</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> : <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="group_2.html#D1">GROUP_2:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:10_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="group_2.html#K1">"</a> 
 ;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:10_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K3">"</a>  &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E4:10_1"/>
<font color="Maroon">a</font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="group_1.html#T19">GROUP_1:19</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:10"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E4:10"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="group_1.html#T19">GROUP_1:19</a></i>;<br/>
<b>hence </b><a NAME="E5:10"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="group_2.html#K1">"</a> 
 <b>by </b><i>, </i>;<br/>


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