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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th22</font></span>: <a NAME="T22"><span class="comment"><font color="firebrick">:: LIOUVIL1:22</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="liouvil1.html#K1" title="LIOUVIL1:func.1">|_</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b2">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">n</font></div></div>
