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<div><span class="kw">theorem </span><a NAME="T146"><span class="comment"><font color="firebrick">:: GROUP_2:146</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">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  <a href="group_2.html#K15" title="GROUP_2:func.15">Left_Cosets</a> <font color="Olive" title="b2">H</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  holds <br/>(  ex <font color="Olive" title="b3">B</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">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_2.html#K15" title="GROUP_2:func.15">Left_Cosets</a> <font color="Olive" title="b2">H</font> &amp;  <a href="group_2.html#K18" title="GROUP_2:func.18">index</a> <font color="Olive" title="b2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">B</font> ) &amp;  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_2.html#K16" title="GROUP_2:func.16">Right_Cosets</a> <font color="Olive" title="b2">H</font> &amp;  <a href="group_2.html#K18" title="GROUP_2:func.18">index</a> <font color="Olive" title="b2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">C</font> ) )</div></div>
