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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><b>that </b><br/><a NAME="E1:98"/><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> 
 <b>and </b><br/><a NAME="E2:98"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<a NAME="E3:98"/>
 <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="group_6.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E4:98"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font>
 
;<br/>
<a NAME="E5:98"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">H</font> is <a href="group_1.html#V6">finite</a> &amp; <font color="Maroon">G</font> is <a href="group_1.html#V6">finite</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">cH</font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:98"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">cH</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> &amp;  <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">cH</font> )
 <b>by </b><i><a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<b>consider </b><font color="Maroon">cG</font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:98"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">cG</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> &amp;  <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">cG</font> )
 <b>by </b><i>, <a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<b>thus </b><a NAME="E10:98"/>
 <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="txt" href="group_6.html#E9:98"><i><font color="Green">E73</font></i></a>, , <a class="ref" href="group_6.html#D2" target="_self">Def2</a></i>;<br/>


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