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





<b>thus </b><a NAME="E1:74"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="group_3.html#R1" target="_self">are_conjugated</a>  implies  ex <font color="Olive">g</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Olive">g</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<b>given </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><a NAME="E1:74_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">g</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_3.html#D7" target="_self">GROUP_3:def 7</a><br/>

<a NAME="E2:74_1"/>
<font color="Maroon">a</font> <a href="group_3.html#K2" target="_self">|^</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T19" target="_self">Th19</a>, </i>;<br/>
<b>hence </b><a NAME="E3:74_1"/>
 ex <font color="Olive">g</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Olive">g</font>
 ;<br/>


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

<b>given </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><a NAME="E2:74"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E3:74"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_3.html#K2" target="_self">|^</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="group_3.html#T19" target="_self">Th19</a>, </i>;<br/>
<b>hence </b><a NAME="E4:74"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="group_3.html#R1" target="_self">are_conjugated</a> 
 <b>by </b><i/>;<br/>


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