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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: COMSEQ_3:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq1</font>, <font color="Olive" title="b2">seq2</font> being   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a> holds  <span class="p1">(<span class="default"><a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <font color="Olive" title="b1">seq1</font></span>)</span> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <font color="Olive" title="b2">seq2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">seq1</font> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <font color="Olive" title="b2">seq2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="series_1.html#T5" onmouseover="rs('series_1/T5')" onmouseout="rh()">SERIES_1:5</a></span>;<br/></div></div>
