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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th42</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: DBLSEQ_3:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <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#K9" title="DBLSEQ_3:func.9">Partial_Sums_in_cod2</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K1" title="DBLSEQ_3:func.1">-</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="dblseq_3.html#K1" title="DBLSEQ_3:func.1">-</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K9" title="DBLSEQ_3:func.9">Partial_Sums_in_cod2</a> <font color="Olive" title="b1">f</font></span>)</span> &amp;  <a href="dblseq_3.html#K10" title="DBLSEQ_3:func.10">Partial_Sums_in_cod1</a> <span class="p1">(<span class="default"><a href="dblseq_3.html#K1" title="DBLSEQ_3:func.1">-</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="dblseq_3.html#K1" title="DBLSEQ_3:func.1">-</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> )</div></div>
