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<b>let </b><font color="Maroon">H</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">H</font>,<font color="Maroon">G</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:84"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">h</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K2">"</a> 
 ;<br/>

<a NAME="E3:84"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">h</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:84"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">g1</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T62">FUNCT_1:62</a></i>;<br/>
<a NAME="E5:84"/><i><font color="Green">E53</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> <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><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:84"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font>
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#T55">FUNCT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E7:84"/>
<font color="Maroon">g1</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i>, , </i>;<br/>


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