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<b>let </b><font color="Maroon" title="c1">seq</font>, <font color="Maroon" title="c2">seq1</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c2">seq1</font> is    <a href="valued_0.html#M1" title="VALUED_0:mode.1">subsequence</a> of <font color="Maroon" title="c1">seq</font> implies <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:45"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>and </b><br/><a NAME="E2:45"/><i><font color="Green" title="E36">A2</font></i>: 
<font color="Maroon" title="c2">seq1</font> is    <a href="valued_0.html#M1" title="VALUED_0:mode.1">subsequence</a> of <font color="Maroon" title="c1">seq</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a></span><br/>

<b>thus </b><a NAME="E3:45"/>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>
 <b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="#E2:45"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="seqm_3.html#T56" target="_self" title="SEQM_3:th.56">Th56</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_2.html#D8" title="SEQ_2:def.8">SEQ_2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a></span><br/>

<b>thus </b><a NAME="E4:45"/>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>
 <b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="#E2:45"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="seqm_3.html#T57" target="_self" title="SEQM_3:th.57">Th57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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