<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">CS</font> be    <a href="closure1.html#L1" target="_self">MSClosureStr</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:61_1_1"/>
<font color="Maroon">CS</font> is <a href="closure1.html#V9" target="_self">absolutely-multiplicative</a>
 ;<br/>

<a NAME="E2:61_1_1"/><b>then </b><i><font color="Green">E34</font></i>: 
the <a href="closure1.html#U1" target="_self">Family</a> of <font color="Maroon">CS</font> is <a href="mssubfam.html#V4">absolutely-multiplicative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:61_1_1"/>
for <font color="Olive">I</font> being   <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">M</font> being   <a href="pboole.html#M1">ManySortedSet</a> of <font color="Olive">I</font><br/> for <font color="Olive">a</font> being <a href="mssubfam.html#V4">absolutely-multiplicative</a> <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Olive">M</font> holds  <font color="Olive">a</font> is <a href="mssubfam.html#V5">properly-upper-bound</a>
 
;<br/>
<b>hence </b><a NAME="E4:61_1_1"/>
the <a href="closure1.html#U1" target="_self">Family</a> of <font color="Maroon">CS</font> is <a href="mssubfam.html#V5">properly-upper-bound</a>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D10" target="_self">CLOSURE1:def 10</a><br/>


</div>
