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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: SERIES_1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>  st (  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> (  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">s1</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">n</font> &amp; <font color="Olive" title="b1">s1</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">s2</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">n</font> ) ) &amp; <font color="Olive" title="b2">s2</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  holds <br/>( <font color="Olive" title="b1">s1</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  &amp;  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <font color="Olive" title="b1">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <font color="Olive" title="b2">s2</font> )</div></div>
