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<div><span class="kw">theorem </span><a NAME="T133"><span class="comment"><font color="firebrick">:: GROUP_3:133</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>  st (  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Olive" title="b2">a</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  or  <a href="group_2.html#K15" title="GROUP_2:func.15">Left_Cosets</a> <span class="p1">(<span class="default"><a href="group_3.html#K10" title="GROUP_3:func.10">Normalizer</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) holds <br/> ex <font color="Olive" title="b3">C</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_3.html#K7" title="GROUP_3:func.7">con_class</a> <font color="Olive" title="b2">a</font> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_2.html#K18" title="GROUP_2:func.18">index</a> <span class="p1">(<span class="default"><a href="group_3.html#K10" title="GROUP_3:func.10">Normalizer</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> )</div></div>
