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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:3"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:3"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font>]
 
<b>by </b><i><a class="txt" href="goboard2.html#E3"><i><font color="Green">Lemma3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:3"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="seq_4.html#V1">bounded_above</a> &amp;  <a href="seq_4.html#K4">upper_bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="seq_4.html#V2">bounded_below</a> &amp;  <a href="seq_4.html#K5">lower_bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="goboard2.html#E1:3"><i><font color="Green">E5</font></i></a></i>;<br/>


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