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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: NAT_5:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">I</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">I</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b4">J</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> holds <br/> <a href="uproots.html#K2" title="UPROOTS:func.2">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="nat_5.html#K1" title="NAT_5:func.1">|</a> <font color="Olive" title="b4">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">Sum</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b4">J</font>)</div></div>
