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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><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#NM1">Element</a> of <font color="Maroon">G</font>;<br/>





<b>thus </b><a NAME="E1:82"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="group_3.html#K7" target="_self">con_class</a> <font color="Maroon">a</font> implies  ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font>,<font color="Olive">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</a>  ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:82_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="group_3.html#K7" target="_self">con_class</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:82_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> <a href="group_3.html#K5" target="_self">|^</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <span class="p2">(<span class="default"><a href="group_2.html#K6">(Omega).</a> <font color="Maroon">G</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:82_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b</font> where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> : <font color="Maroon">a</font>,<font color="Olive">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</a>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="group_3.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E4:82_1"/>
 ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font>,<font color="Olive">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</a>  )
 ;<br/>


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

<b>given </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><a NAME="E2:82"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</a>  )
 ;<br/>

<a NAME="E3:82"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">c</font> where <font color="Olive">c</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> : <font color="Maroon">a</font>,<font color="Olive">c</font> <a href="group_3.html#R2" target="_self">are_conjugated</a>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="group_3.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E4:82"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> <a href="group_3.html#K5" target="_self">|^</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <span class="p2">(<span class="default"><a href="group_2.html#K6">(Omega).</a> <font color="Maroon">G</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="group_3.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="group_3.html#K7" target="_self">con_class</a> <font color="Maroon">a</font>
 ;<br/>


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