<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<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/>





<a NAME="E1:23"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K14">Left_Cosets</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="group_2.html#D15">GROUP_2:def 15</a></i>;<br/>
<a NAME="E2:23"/>
<font color="Maroon">N</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K15">Right_Cosets</a> <font color="Maroon">N</font>
 
<b>by </b><i><a class="ref" href="group_2.html#D16">GROUP_2:def 16</a></i>;<br/>
<b>hence </b><a NAME="E3:23"/>
( <font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="group_6.html#K4" target="_self">Cosets</a> <font color="Maroon">N</font> &amp; <font color="Maroon">N</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="group_6.html#K4" target="_self">Cosets</a> <font color="Maroon">N</font> )
 <b>by </b><i>, </i>;<br/>


</div>
