<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T24"><span class="comment"><font color="firebrick">:: SEQ_4:24</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="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp;  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <font color="Olive" title="b1">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b2">seq1</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> st <br/>( <font color="Olive" title="b2">seq1</font> is    <a href="valued_0.html#M2" title="VALUED_0:mode.2">subsequence</a> of <font color="Olive" title="b1">seq</font> &amp; <font color="Olive" title="b2">seq1</font> is  <a href="ordinal1.html#V9" title="ORDINAL1:attr.9">non-zero</a>  )</div></div>
