<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: SEQM_3:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">seq</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> holds <br/> ( ( <font color="Olive" title="b2">seq</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">r</font> implies <font color="Olive" title="b1">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b2">seq</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  ) &amp; (  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> implies <font color="Olive" title="b1">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b2">seq</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  ) &amp; ( <font color="Olive" title="b2">seq</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b1">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b2">seq</font> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">decreasing</a>  ) )</div></div>
