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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">H</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:69"/>
<font color="Maroon">H</font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:69"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> &amp;  <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<b>assume </b><a NAME="E4:69"/>
 <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:69"/><i><font color="Green">E36</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="card_2.html#T60">CARD_2:60</a></i>;<br/>
<a NAME="E7:69"/>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:69"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E9:69"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:69"/>
<font color="Maroon">H</font> <a href="group_2.html#R1" target="_self">=</a>  <a href="group_2.html#K5" target="_self">(1).</a> <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/>


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