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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: MEASUR12:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span>)</span><br/>  for <font color="Olive" title="b2">G</font> being    <a href="measur12.html#M2" title="MEASUR12:mode.2">Open_Interval_Covering</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">H</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds <br/> <a href="measure7.html#K11" title="MEASURE7:func.11">On</a> (<font color="Olive" title="b2">G</font>,<font color="Olive" title="b3">H</font>) is    <a href="measur12.html#M1" title="MEASUR12:mode.1">Open_Interval_Covering</a> of  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">F</font></span>)</span></div></div>
