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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:99"/><i><font color="Green" title="E65">A1</font></i>: 
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 <b>and </b><br/><a NAME="E2:99"/><i><font color="Green" title="E66">A2</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ;<br/>

<a NAME="E3:99"/><i><font color="Green" title="E67">A3</font></i>: 
 <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c2">H</font>
 
<b>by </b><i><a class="txt" href="group_6.html#E1:99"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="group_6.html#T84" target="_self" title="GROUP_6:th.84">Th84</a></i>;<br/>
<a NAME="E4:99"/>
( <font color="Maroon" title="c2">H</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> &amp; <font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )
 
<b>by </b><i><a class="txt" href="group_6.html#E1:99"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="group_6.html#E2:99"><i><font color="Green" title="E66">A2</font></i></a>, <a class="ref" href="group_6.html#T85" target="_self" title="GROUP_6:th.85">Th85</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">cH</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:99"/><i><font color="Green" title="E68">A4</font></i>: 
( <font color="Maroon" title="c3">cH</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H</font> &amp;  <a href="group_1.html#K9" title="GROUP_1:func.9">ord</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">cH</font> )
 <b>by </b><i><a class="ref" href="group_1.html#D15" title="GROUP_1:def.15">GROUP_1:def 15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">cG</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:99"/><i><font color="Green" title="E69">A5</font></i>: 
( <font color="Maroon" title="c4">cG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="group_1.html#K9" title="GROUP_1:func.9">ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c4">cG</font> )
 <b>by </b><i><a class="txt" href="group_6.html#E2:99"><i><font color="Green" title="E66">A2</font></i></a>, <a class="ref" href="group_1.html#D15" title="GROUP_1:def.15">GROUP_1:def 15</a></i>;<br/>
<b>thus </b><a NAME="E9:99"/>
 <a href="group_1.html#K9" title="GROUP_1:func.9">ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K9" title="GROUP_1:func.9">ord</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="group_6.html#E3:99"><i><font color="Green" title="E67">A3</font></i></a>, <a class="txt" href="group_6.html#E6:99"><i><font color="Green" title="E68">A4</font></i></a>, <a class="txt" href="group_6.html#E8:99"><i><font color="Green" title="E69">A5</font></i></a></i>;<br/>


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