<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th19</font></span>: <a NAME="T22"><span class="comment"><font color="firebrick">:: COUSIN2:22</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="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">D</font> being    <a href="integra1.html#M1" title="INTEGRA1:mode.1">Division</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">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>  st <font color="Olive" title="b3">f</font> is  <a href="integra1.html#V1" title="INTEGRA1:attr.1">upper_integrable</a>  holds <br/> <a href="integra1.html#K10" title="INTEGRA1:func.10">upper_integral</a> <font color="Olive" title="b3">f</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="integra1.html#K6" title="INTEGRA1:func.6">upper_sum</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">D</font>)</div></div>
