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<b>let </b><font color="Maroon">G</font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<br/>

<a NAME="E1:29"/>
for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <span class="p1">(<span class="default"><a href="autgroup.html#K6" target="_self">Conjugate</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

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

<a NAME="E1:29_1"/>
<font color="Maroon">a</font> <a href="group_3.html#K2">|^</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T24">GROUP_3:24</a></i>;<br/>
<b>hence </b><a NAME="E2:29_1"/>
<span class="p1">(<span class="default"><a href="autgroup.html#K6" target="_self">Conjugate</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:29"/><b>then </b><i><font color="Green">E23</font></i>: 
for <font color="Olive">q</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> holds <br/><span class="p1">(<span class="default"><a href="autgroup.html#K6" target="_self">Conjugate</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">q</font>
 
;<br/>
<a NAME="E3:29"/>
 <a href="autgroup.html#K6" target="_self">Conjugate</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> is    <a href="fraenkel.html#M2">Element</a> of  <a href="autgroup.html#K1" target="_self">Aut</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:29"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="autgroup.html#K6" target="_self">Conjugate</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:29"/>
 <a href="autgroup.html#K6" target="_self">Conjugate</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 <b>by </b><i><a class="txt" href="autgroup.html#E2"><i><font color="Green">Lemma27</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>


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