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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/><b>let </b><font color="Maroon">f</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="autgroup.html#K1" target="_self">Aut</a> <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="autgroup.html#K3" target="_self">AutGroup</a> <font color="Maroon">G</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:14"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 ;<br/>

<b>consider </b><font color="Maroon">g1</font> being    <a href="fraenkel.html#M2">Element</a> of  <a href="autgroup.html#K1" target="_self">Aut</a> <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:14"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K3">"</a> 
 ;<br/>
<i><font color="Green">E25</font></i>:  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> = 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
<b>by </b><i/>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
<b>by </b><i/>
;<br/>
<a NAME="E5:14"/>
<font color="Maroon">f</font> is   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:14"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i/>;<br/>
<a NAME="E7:14"/>
<font color="Maroon">g1</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">g</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E8:14"/><b>then </b>
<font color="Maroon">g1</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="autgroup.html#K3" target="_self">AutGroup</a> <font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_1.html#D6">GROUP_1:def 6</a></i>;<br/>
<a NAME="E9:14"/><b>then </b>
<font color="Maroon">g1</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <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/>;<br/>
<b>hence </b><a NAME="E10:14"/>
<font color="Maroon">f</font> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K3">"</a> 
 <b>by </b><i>, , , <a class="ref" href="funct_2.html#T36">FUNCT_2:36</a></i>;<br/>


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