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<div><span class="kw">theorem </span><a NAME="T50"><span class="comment"><font color="firebrick">:: DBLSEQ_3:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</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> holds   <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#K2" title="DBLSEQ_3:func.2">+</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#K3" title="MESFUNC1:func.3">+</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></div></div>
