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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="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>





<a NAME="E1:121"/>
(  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font> &amp;  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">G</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="group_2.html#T132" target="_self" title="GROUP_2:th.132">Th132</a></i>;<br/>
<b>hence </b><a NAME="E2:121"/>
(  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp;  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c3">H</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c2">a</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 <b>by </b><i><a class="ref" href="group_2.html#T151" target="_self" title="GROUP_2:th.151">Th151</a>, <a class="ref" href="group_2.html#T153" target="_self" title="GROUP_2:th.153">Th153</a></i>;<br/>


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