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

<a NAME="E1:25"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K4" target="_self">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K4" target="_self">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E2:25"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="seq_4.html#V1">bounded_above</a> iff  <a href="pscomp_1.html#K4" target="_self">-</a> <font color="Maroon">c<sub>1</sub></font> is <a href="seq_4.html#V2">bounded_below</a> )
 <b>by </b><i><a class="txt" href="pscomp_1.html#E22"><i><font color="Green">Lemma14</font></i></a>, <a class="txt" href="pscomp_1.html#E23"><i><font color="Green">Lemma15</font></i></a></i>;<br/>


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