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<div class="add">

<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="E1:96"/>
( <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span> <a href="group_3.html#R4" target="_self">are_conjugated</a>  implies <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:96_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span> <a href="group_3.html#R4" target="_self">are_conjugated</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="E3:96_1"/><i><font color="Green">E38</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> <a href="group_3.html#K4" target="_self">|^</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="group_3.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E4:96_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">g</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="group_3.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E5:96_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T6">ZFMISC_1:6</a></i>;<br/>
<b>hence </b><a NAME="E6:96_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</a> 
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:96"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="group_3.html#R2" target="_self">are_conjugated</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="E4:96"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">a</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:96"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> <a href="group_3.html#K4" target="_self">|^</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T30" target="_self">Th30</a>, </i>;<br/>
<b>hence </b><a NAME="E6:96"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span> <a href="group_3.html#R4" target="_self">are_conjugated</a> 
 <b>by </b><i><a class="ref" href="group_3.html#T25" target="_self">Th25</a></i>;<br/>


</div>
