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

<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">H</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><a NAME="E1:128"/>
<font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ;<br/>

<a NAME="E2:128"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a></i>;<br/>
<a NAME="E3:128"/><b>then </b>
(  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp;  <a href="group_2.html#K15" title="GROUP_2:func.15">Right_Cosets</a> <font color="Maroon" title="c2">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="group_2.html#K14" title="GROUP_2:func.14">Left_Cosets</a> <font color="Maroon" title="c2">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> )
 
<b>by </b><i><a class="ref" href="finset_1.html#T24" title="FINSET_1:th.24">FINSET_1:24</a></i>;<br/>
<b>hence </b><a NAME="E4:128"/>
(  <a href="group_2.html#K15" title="GROUP_2:func.15">Right_Cosets</a> <font color="Maroon" title="c2">H</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp;  <a href="group_2.html#K14" title="GROUP_2:func.14">Left_Cosets</a> <font color="Maroon" title="c2">H</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 <b>by </b><i><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a></i>;<br/>


</div>
