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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:64"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<a NAME="E2:64"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font> is <a href="group_1.html#V6">finite</a>
 
<b>by </b><i><a class="ref" href="group_3.html#T78" target="_self">Th78</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:64"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:64"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="group_3.html#E1:64"><i><font color="Green">E51</font></i></a>, <a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>
<a NAME="E7:64"/>
(  <a href="group_1.html#K8">Ord</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="group_1.html#K8">Ord</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K8">Ord</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="group_1.html#K8">Ord</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="group_3.html#T77" target="_self">Th77</a></i>;<br/>
<b>hence </b><a NAME="E8:64"/>
 <a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="group_3.html#E4:64"><i><font color="Green">E52</font></i></a>, <a class="txt" href="group_3.html#E6:64"><i><font color="Green">E53</font></i></a></i>;<br/>


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