<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">Th34</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: MEASUR12:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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 <font color="Olive" title="b1">H</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">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/> for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  ex <font color="Olive" title="b3">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <br/> for <font color="Olive" title="b4">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="b5">G</font> being    <a href="measur12.html#M2" title="MEASUR12:mode.2">Open_Interval_Covering</a> of <font color="Olive" title="b4">F</font> holds  <span class="p1">(<span class="default"><a href="supinf_2.html#K16" title="SUPINF_2:func.16">Ser</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measure7.html#K11" title="MEASURE7:func.11">On</a> (<font color="Olive" title="b5">G</font>,<font color="Olive" title="b1">H</font>)</span>)</span> <a href="measure7.html#K3" title="MEASURE7:func.3">vol</a></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K16" title="SUPINF_2:func.16">Ser</a> <span class="p2">(<span class="default"><a href="measure7.html#K7" title="MEASURE7:func.7">vol</a> <font color="Olive" title="b5">G</font></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">m</font></div></div>
