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<div><span class="kw">theorem </span><a NAME="T37"><span class="comment"><font color="firebrick">:: SEQ_4:37</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>  st <font color="Olive" title="b1">seq</font> is  <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>  &amp; <font color="Olive" title="b1">seq</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">V47</a>() holds <br/> for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b1">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <font color="Olive" title="b1">seq</font></div></div>
