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<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: TOPRNS_1:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">seq</font> being   <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Olive" title="b1">N</font>  st <font color="Olive" title="b2">seq</font> is  <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>  holds <br/><font color="Olive" title="b2">seq</font> is  <a href="toprns_1.html#V2" title="TOPRNS_1:attr.2">bounded</a> </div></div>
