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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: PROB_4:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">Eseq</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>  st <font color="Olive" title="b1">seq</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">Eseq</font> &amp; <font color="Olive" title="b1">seq</font> is  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative</a>  &amp; <font color="Olive" title="b1">seq</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  holds <br/> <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <font color="Olive" title="b1">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">SUM</a> <font color="Olive" title="b2">Eseq</font></div></div>
