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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th48</font></span>: <a NAME="T48"><span class="comment"><font color="firebrick">:: MESFUN11:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">F</font> <a href="mesfunc5.html#K3" title="MESFUNC5:func.3">#</a> <font color="Olive" title="b3">x</font> is  <a href="mesfunc9.html#V1" title="MESFUNC9:attr.1">summable</a>  holds <br/>( <span class="p1">(<span class="default"><a href="mesfun11.html#K3" title="MESFUN11:func.3">-</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="mesfunc5.html#K3" title="MESFUNC5:func.3">#</a> <font color="Olive" title="b3">x</font> is  <a href="mesfunc9.html#V1" title="MESFUNC9:attr.1">summable</a>  &amp;  <a href="mesfunc9.html#K2" title="MESFUNC9:func.2">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun11.html#K3" title="MESFUN11:func.3">-</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="mesfunc5.html#K3" title="MESFUNC5:func.3">#</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K2" title="SUPINF_2:func.2">-</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K2" title="MESFUNC9:func.2">Sum</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">F</font> <a href="mesfunc5.html#K3" title="MESFUNC5:func.3">#</a> <font color="Olive" title="b3">x</font></span>)</span></span>)</span> )</div></div>
