<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T273"><span class="comment"><font color="firebrick">:: GROUP_1A:273</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1a.html#NM1" title="GROUP_1A:NM.1">addGroup</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_1a.html#M1" title="GROUP_1A:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font>  st  <a href="group_1a.html#K20" title="GROUP_1A:func.20">Left_Cosets</a> <font color="Olive" title="b3">H</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  holds <br/> <a href="group_1a.html#K23" title="GROUP_1A:func.23">index</a> <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1a.html#K23" title="GROUP_1A:func.23">index</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="group_1a.html#K29" title="GROUP_1A:func.29">*</a> <font color="Olive" title="b2">a</font></span>)</span></div></div>
