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

<b>let </b><font color="Maroon" title="c2">CS</font> be    <a href="closure2.html#L1" title="CLOSURE2:struct.1">ClosureStr</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">CS</font> is <a href="closure2.html#V15" title="CLOSURE2:attr.15">absolutely-multiplicative</a> implies <font color="Maroon" title="c2">CS</font> is <a href="closure2.html#V16" title="CLOSURE2:attr.16">properly-upper-bound</a> )</span><br/>

<b>assume </b><a NAME="E1:88_1_1"/>
<font color="Maroon" title="c2">CS</font> is <a href="closure2.html#V15" title="CLOSURE2:attr.15">absolutely-multiplicative</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">CS</font> is <a href="closure2.html#V16" title="CLOSURE2:attr.16">properly-upper-bound</a></span><br/>

<a NAME="E2:88_1_1"/><b>then </b><i><font color="Green" title="E35">A1</font></i>: 
the <a href="closure2.html#U1" title="CLOSURE2:sel.1">Family</a> of <font color="Maroon" title="c2">CS</font> is <a href="closure2.html#V4" title="CLOSURE2:attr.4">absolutely-multiplicative</a>
 
;<br/>
<b>thus </b><a NAME="E3:88_1_1"/>
the <a href="closure2.html#U1" title="CLOSURE2:sel.1">Family</a> of <font color="Maroon" title="c2">CS</font> is <a href="closure2.html#V5" title="CLOSURE2:attr.5">properly-upper-bound</a>
 <b>by </b><i><a class="txt" href="#E2:88_1_1"><i><font color="Green" title="E35">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure2.html#D20" target="_self" title="CLOSURE2:def.20">CLOSURE2:def 20</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
