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<span class="kw">let </span><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is  <a href="valued_0.html#V10" title="VALUED_0:attr.10">non-increasing</a>  &amp; <font color="Maroon" title="c1">seq</font> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>  implies <font color="Maroon" title="c1">seq</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:28"/>
( <font color="Maroon" title="c1">seq</font> is  <a href="valued_0.html#V10" title="VALUED_0:attr.10">non-increasing</a>  &amp; <font color="Maroon" title="c1">seq</font> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> </span><br/>

<a NAME="E2:28"/><span class="kw">then </span>
( <font color="Maroon" title="c1">seq</font> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>  &amp; <font color="Maroon" title="c1">seq</font> is  <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="limfunc1.html#T26" title="LIMFUNC1:th.26">LIMFUNC1:26</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:28"/>
<font color="Maroon" title="c1">seq</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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