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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:3_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ;<br/><a NAME="E3:3_1"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="card_1.html#D11">CARD_1:def 11</a></i>;<br/><b>hence </b><a NAME="E4:3_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><a NAME="E2:3"/><i><font color="Green">E4</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E3:3"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="txt" href="card_4.html#E2:3"><i><font color="Green">E4</font></i></a>, <a class="ref" href="card_4.html#T1" target="_self">Th1</a></i>;<br/>


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