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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<a NAME="E1:32"/>
<font color="Maroon">seq</font> <a href="seqm_3.html#K1">^\</a> <font color="Maroon">k</font> is    <a href="seqm_3.html#M1">subsequence</a> of <font color="Maroon">seq</font>
 
<b>by </b><i><a class="ref" href="seqm_3.html#T47">SEQM_3:47</a></i>;<br/>
<b>hence </b><a NAME="E2:32"/>
( <font color="Maroon">seq</font> is <a href="seq_2.html#V2">bounded_below</a> implies <font color="Maroon">seq</font> <a href="seqm_3.html#K1">^\</a> <font color="Maroon">k</font> is <a href="seq_2.html#V2">bounded_below</a> )
 <b>by </b><i><a class="ref" href="seqm_3.html#T57">SEQM_3:57</a></i>;<br/>


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