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<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_1.html#NM1">Group</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:97"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">G</font>,<font color="Maroon">H</font> <a href="group_6.html#R1" target="_self">are_isomorphic</a> 
 <b>and </b><br/><a NAME="E2:97"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<b>consider </b><font color="Maroon">h</font> being   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font><b> such that </b><br/><a NAME="E4:97"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">h</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i>, </i>;<br/>
<a NAME="E5:97"/>
<font color="Maroon">h</font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 
<b>by </b><i>, <a class="ref" href="group_6.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E6:97"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="relset_1.html#K5">rng</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">H</font>
 
<b>by </b><i><a class="txt" href="group_6.html#E6:97"><i><font color="Green">E52</font></i></a></i>;<br/>
<a NAME="E7:97"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, <a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>
<a NAME="E8:97"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:97"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, <a class="ref" href="finset_1.html#T26">FINSET_1:26</a></i>;<br/>
<b>hence </b><a NAME="E10:97"/>
<font color="Maroon">H</font> is <a href="group_1.html#V6">finite</a>
 <b>by </b><i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>


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