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<b>let </b><font color="Maroon">G</font> be  <a href="group_1.html#V1">strict</a> <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><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E36</font></i>: 
 <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font>
 ;<br/>

<a NAME="E3:72"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">H</font> is <a href="group_1.html#V6">finite</a>
 
<b>by </b><i><a class="txt" href="group_2.html#E7:72"><i><font color="Green">E50</font></i></a>, <a class="ref" href="group_2.html#T3" target="_self">Th3</a></i>;<br/>
<b>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="E5:72"/><i><font color="Green">E49</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">G</font> &amp;  <a href="group_1.html#K9">ord</a> <font color="Maroon">G</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="txt" href="group_2.html#E7:72"><i><font color="Green">E50</font></i></a>, <a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<b>consider </b><font color="Maroon">C</font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:72"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">C</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">C</font> )
 <b>by </b><i>, <a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<a NAME="E8:72"/><i><font color="Green">E51</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<a NAME="E9:72"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:72_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 ;<br/>

<a NAME="E2:72_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> <a href="xboole_0.html#R2">c&lt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:72_1"/>
contradiction
 <b>by </b><i><a class="txt" href="group_2.html#E8:72"><i><font color="Green">E51</font></i></a>, , , <a class="ref" href="card_2.html#T67">CARD_2:67</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:72"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/>


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