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<div><span class="kw">theorem </span><a NAME="T71"><span class="comment"><font color="firebrick">:: DBLSEQ_3:71</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</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>  st  <a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V5" title="DBLSEQ_3:attr.5">convergent_in_cod1_to_-infty</a>  holds <br/> ex <font color="Olive" title="b2">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st  <a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p1">(<span class="default"><a href="dblseq_3.html#K10" title="DBLSEQ_3:func.10">Partial_Sums_in_cod1</a> <font color="Olive" title="b1">f</font></span>)</span>,<font color="Olive" title="b2">m</font>) is  <a href="mesfunc5.html#V9" title="MESFUNC5:attr.9">convergent_to_-infty</a> </div></div>
