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<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font>;<br/>





<b>thus </b><a NAME="E1:82"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Maroon" title="c3">a</font> implies  ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">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="82_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:82_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Maroon" title="c3">a</font>
 ;<br/>

<a NAME="E2:82_1"/><b>then </b>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">b</font> where <font color="Olive" title="b1">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a>  </span>}</span> 
 
<b>by </b><i><a class="ref" href="group_3.html#T93" target="_self" title="GROUP_3:th.93">Th93</a></i>;<br/>
<b>hence </b><a NAME="E3:82_1"/>
 ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a>  )
 ;<br/>


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

<b>given </b><font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><a NAME="E3:82"/><i><font color="Green" title="E59">A1</font></i>: 
( <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a>  )
 ;<br/>

<a NAME="E4:82"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">c</font> where <font color="Olive" title="b1">c</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">c</font> <a href="group_3.html#R2" title="GROUP_3:pred.2">are_conjugated</a>  </span>}</span> 
 
<b>by </b><i><a class="txt" href="group_3.html#E3:82"><i><font color="Green" title="E59">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="group_3.html#T93" target="_self" title="GROUP_3:th.93">Th93</a></i>;<br/>


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