<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T40"><span class="comment"><font color="firebrick">:: MEASURE9:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="simplex0.html#NV1" title="SIMPLEX0:NV.1">with_empty_element</a>   <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a>   <a href="srings_3.html#V1" title="SRINGS_3:attr.1">semi-diff-closed</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">P</font> being    <a href="measure9.html#M1" title="MEASURE9:mode.1">pre-Measure</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">F1</font>, <font color="Olive" title="b5">F2</font> being   <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b2">S</font>  st  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b4">F1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> &amp;  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b4">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b5">F2</font> holds <br/><font color="Olive" title="b3">P</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b4">F1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">P</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b5">F2</font></span>)</span> ;<br/></div></div>
