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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th3</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: MESFUN15:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f1</font> being  <a href="mesfunc5.html#V3" title="MESFUNC5:attr.3">V173</a>() <a href="mesfunc5.html#NM1" title="MESFUNC5:NM.1">ExtREAL_sequence</a><br/>  for <font color="Olive" title="b2">f2</font> being  <a href="mesfunc5.html#V4" title="MESFUNC5:attr.4">V174</a>() <a href="mesfunc5.html#NM1" title="MESFUNC5:NM.1">ExtREAL_sequence</a> holds <br/> (  <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="dblseq_3.html#K4" title="DBLSEQ_3:func.4">-</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K1" title="MESFUNC9:func.1">Partial_Sums</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="dblseq_3.html#K4" title="DBLSEQ_3:func.4">-</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K1" title="MESFUNC9:func.1">Partial_Sums</a> <font color="Olive" title="b2">f2</font></span>)</span> &amp;  <a href="mesfunc9.html#K1" title="MESFUNC9:func.1">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="dblseq_3.html#K5" title="DBLSEQ_3:func.5">-</a> <font color="Olive" title="b1">f1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K1" title="MESFUNC9:func.1">Partial_Sums</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="dblseq_3.html#K5" title="DBLSEQ_3:func.5">-</a> <span class="p1">(<span class="default"><a href="mesfunc9.html#K1" title="MESFUNC9:func.1">Partial_Sums</a> <font color="Olive" title="b1">f1</font></span>)</span> )</div></div>
