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<div class="add">

<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>thus </b><a NAME="E1:96"/>
( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  implies <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">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" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:96_1"/><i><font color="Green" title="E67">A1</font></i>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_3.html#K4" title="GROUP_3:func.4">|^</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="group_3.html#T104" target="_self" title="GROUP_3:th.104">Th104</a></i>;<br/>
<a NAME="E4:96_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c4">g</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="group_3.html#E3:96_1"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="group_3.html#T44" target="_self" title="GROUP_3:th.44">Th44</a></i>;<br/>
<a NAME="E5:96_1"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c4">g</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T6" title="ZFMISC_1:th.6">ZFMISC_1:6</a></i>;<br/>
<b>hence </b><a NAME="E6:96_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a> 
 <b>by </b><i><a class="ref" href="group_3.html#T88" target="_self" title="GROUP_3:th.88">Th88</a></i>;<br/>


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

<b>assume </b><a NAME="E2:96"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:96"/><i><font color="Green" title="E67">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="group_3.html#T88" target="_self" title="GROUP_3:th.88">Th88</a></i>;<br/>
<a NAME="E5:96"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_3.html#K4" title="GROUP_3:func.4">|^</a> <font color="Maroon" title="c4">g</font>
 
<b>by </b><i><a class="txt" href="group_3.html#E4:96"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="group_3.html#T44" target="_self" title="GROUP_3:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E6:96"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a> 
 <b>by </b><i><a class="ref" href="group_3.html#T104" target="_self" title="GROUP_3:th.104">Th104</a></i>;<br/>


</div>
