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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">H</font> be  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c3">H</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<a NAME="E2:66"/><i><font color="Green" title="E48">A2</font></i>: 
 <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <span class="p1">(<span class="default"><a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="group_2.html#T81" title="GROUP_2:th.81">GROUP_2:81</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">H</font> = <font color="Maroon" title="c3">H</font> as  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="group_3.html#E1:66"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="group_3.html#T78" target="_self" title="GROUP_3:th.78">Th78</a></i>;<br/>
<a NAME="E4:66"/>
 <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="group_3.html#E1:66"><i><font color="Green" title="E47">A1</font></i></a>, <a class="txt" href="group_3.html#E2:66"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="group_3.html#T77" target="_self" title="GROUP_3:th.77">Th77</a></i>;<br/>
<b>hence </b><a NAME="E5:66"/>
<font color="Maroon" title="c3">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="group_2.html#T82" title="GROUP_2:th.82">GROUP_2:82</a></i>;<br/>


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