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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>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <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="E2:9"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">f</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">f</font> <a href="funct_1.html#K2">"</a>  as   <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="E4:9"/>
<font color="Maroon">A</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 
<b>by </b><i>, <a class="ref" href="group_6.html#T73">GROUP_6:73</a></i>;<br/>
<a NAME="E5:9"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">A</font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a>  &amp; <font color="Maroon">A</font> <a href="group_6.html#NR1" target="_self">is_monomorphism</a>  )
 
<b>by </b><i><a class="ref" href="group_6.html#D14">GROUP_6:def 14</a></i>;<br/>
<a NAME="E6:9"/><b>then </b>
<font color="Maroon">A</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="group_6.html#D12">GROUP_6:def 12</a></i>;<br/>
<b>hence </b><a NAME="E7:9"/>
<font color="Maroon">f</font> <a href="funct_1.html#K2">"</a>  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>, </i>;<br/>


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