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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th28</font></span>: <a NAME="T28"><span class="comment"><font color="firebrick">:: NAT_5:28</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</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>, <font color="Olive" title="b5">K</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> holds   <a href="uproots.html#K2" title="UPROOTS:func.2">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K24" title="BINOP_2:func.24">multnat</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span></span>)</span> <a href="nat_5.html#K1" title="NAT_5:func.1">|</a> <span class="p2"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><font color="Olive" title="b4">J</font>,<font color="Olive" title="b5">K</font></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K2" title="UPROOTS:func.2">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="nat_5.html#K1" title="NAT_5:func.1">|</a> <font color="Olive" title="b4">J</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="uproots.html#K2" title="UPROOTS:func.2">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">g</font> <a href="nat_5.html#K1" title="NAT_5:func.1">|</a> <font color="Olive" title="b5">K</font></span>)</span></span>)</span></div></div>
