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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: LIMFUNC1:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> holds <br/> ( ( <font color="Olive" title="b1">seq</font> is  <a href="valued_0.html#V9" title="VALUED_0:attr.9">non-decreasing</a>  implies <font color="Olive" title="b1">seq</font> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>  ) &amp; ( <font color="Olive" title="b1">seq</font> is  <a href="valued_0.html#V10" title="VALUED_0:attr.10">non-increasing</a>  implies <font color="Olive" title="b1">seq</font> is  <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>  ) )</div></div>
