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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">N</font> be  <a href="group_3.html#V1">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green">E45</font></i>: 
 <a href="group_2.html#K14">Left_Cosets</a> <font color="Maroon">N</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">LC</font> =  <a href="group_2.html#K14">Left_Cosets</a> <font color="Maroon">N</font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E3:33"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">G</font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">N</font> is <a href="group_1.html#V6">finite</a>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">GN</font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">N</font></span>)</span> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>
<b>thus </b> <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">N</font></span>)</span> = 
 <a href="card_1.html#K4">card</a> <font color="Maroon">LC</font>
<b>by </b><i>, <a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>
<br/>.= 
 <a href="group_2.html#K17">index</a> <font color="Maroon">N</font>
<b>by </b><i><a class="ref" href="group_2.html#D18">GROUP_2:def 18</a></i>
;<br/>


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