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

<b>assume </b><a NAME="E1:96"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">G</font>,<font color="Maroon">H</font> <a href="group_6.html#R2" target="_self">are_isomorphic</a> 
 ;<br/>

<b>then 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="E3:96"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">h</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i/>;<br/>
<a NAME="E4:96"/>
<font color="Maroon">H</font>,<font color="Maroon">G</font> <a href="group_6.html#R2" target="_self">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="group_6.html#T10" target="_self">Th10</a></i>;<br/>
<b>then consider </b><font color="Maroon">g1</font> being   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">H</font>,<font color="Maroon">G</font><b> such that </b><br/><a NAME="E6:96"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">g1</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i/>;<br/>
<a NAME="E7:96"/>
<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="E8:96"/><b>then </b>
 <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E9:96"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="group_1.html#K8">Ord</a> <font color="Maroon">H</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="group_1.html#K8">Ord</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:96"/>
<font color="Maroon">g1</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="E11:96"/><b>then </b>
 <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E12:96"/><b>then </b>
 <a href="group_1.html#K8">Ord</a> <font color="Maroon">G</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="group_1.html#K8">Ord</a> <font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E13:96"/>
 <a href="group_1.html#K8">Ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K8">Ord</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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