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<div><span class="kw">theorem </span><a NAME="T33"><span class="comment"><font color="firebrick">:: COMSEQ_3:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq</font>, <font color="Olive" title="b2">seq1</font> being   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>  st (  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b2">seq1</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ) holds <br/> <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">seq</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <font color="Olive" title="b2">seq1</font></div></div>
