<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T52"><span class="comment"><font color="firebrick">:: DBLSEQ_3:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f1</font> being  <a href="mesfunc5.html#V3" title="MESFUNC5:attr.3">V183</a>() <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b2">f2</font> being  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">V184</a>() <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> (  <a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="dblseq_3.html#K4" title="DBLSEQ_3:func.4">-</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="mesfunc1.html#K4" title="MESFUNC1:func.4">-</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <font color="Olive" title="b2">f2</font></span>)</span> &amp;  <a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="dblseq_3.html#K5" title="DBLSEQ_3:func.5">-</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="mesfunc1.html#K4" title="MESFUNC1:func.4">-</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <font color="Olive" title="b1">f1</font></span>)</span> )</div></div>
