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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">seq1</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">seq</font> is <a href="seq_2.html#V3">bounded</a>
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">seq1</font> is    <a href="seqm_3.html#M1" target="_self">subsequence</a> of <font color="Maroon">seq</font>
 ;<br/>

<a NAME="E3:72"/>
<font color="Maroon">seq</font> is <a href="seq_2.html#V1">bounded_above</a>
 
<b>by </b><i><a class="ref" href="seqm_3.html#D3" target="_self">Def3</a>, <a class="ref" href="seq_2.html#D5">SEQ_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:72"/>
<font color="Maroon">seq1</font> is <a href="seq_2.html#V1">bounded_above</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#D4" target="_self">Def4</a>, <a class="ref" href="seqm_3.html#D1" target="_self">Def1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_2.html#D5">SEQ_2:def 5</a><br/>

<a NAME="E5:72"/>
<font color="Maroon">seq</font> is <a href="seq_2.html#V2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="seqm_3.html#D3" target="_self">Def3</a>, <a class="ref" href="seq_2.html#D5">SEQ_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:72"/>
<font color="Maroon">seq1</font> is <a href="seq_2.html#V2">bounded_below</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#D4" target="_self">Def4</a>, <a class="ref" href="seqm_3.html#D2" target="_self">Def2</a></i>;<br/>


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