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<div><span class="kw">theorem </span><a NAME="T112"><span class="comment"><font color="firebrick">:: GROUP_2:112</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">H</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> holds <br/><font color="Olive" title="b2">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">H</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Olive" title="b2">a</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T25" target="_self" onmouseover="rs('group_2/T25')" onmouseout="rh()">Th25</a></span>;<br/></div></div>
