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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: GROUP_8:19</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">B</font>, <font color="Olive" title="b3">A</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b4">D</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b3">A</font>  st <font color="Olive" title="b4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">A</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  holds <br/> <a href="group_8.html#NK2" title="GROUP_8:NK.2">index</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">B</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="group_8.html#NK2" title="GROUP_8:NK.2">index</a> (<font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">D</font>)</div></div>
