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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: INTEGRA4:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( ( <font color="Olive" title="b2">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Olive" title="b3">r</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span> ) iff <font color="Olive" title="b2">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="rfunct_1.html#K7" title="RFUNCT_1:func.7">chi</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b1">A</font>)</span>)</span> )</div></div>
