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<b>let </b><font color="Maroon" title="c2">CS</font> be    <a href="closure1.html#L1" title="CLOSURE1:struct.1">MSClosureStr</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="closure1.html#V9" title="CLOSURE1:attr.9">absolutely-multiplicative</a> implies <font color="Maroon" title="c2">CS</font> is <a href="closure1.html#V10" title="CLOSURE1:attr.10">properly-upper-bound</a> )</span><br/>

<b>assume </b><a NAME="E1:61_1_1"/>
<font color="Maroon" title="c2">CS</font> is <a href="closure1.html#V9" title="CLOSURE1:attr.9">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="closure1.html#V10" title="CLOSURE1:attr.10">properly-upper-bound</a></span><br/>

<a NAME="E2:61_1_1"/><b>then </b><i><font color="Green" title="E22">A1</font></i>: 
the <a href="closure1.html#U1" title="CLOSURE1:sel.1">Family</a> of <font color="Maroon" title="c2">CS</font> is <a href="mssubfam.html#V4" title="MSSUBFAM:attr.4">absolutely-multiplicative</a>
 
<b>by </b><i><a class="ref" href="closure1.html#D9" target="_self" title="CLOSURE1:def.9">Def9</a></i>;<br/>
<a NAME="E3:61_1_1"/>
for <font color="Olive" title="b1">I</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">M</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/> for <font color="Olive" title="b3">a</font> being <a href="mssubfam.html#V4" title="MSSUBFAM:attr.4">absolutely-multiplicative</a> <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Olive" title="b2">M</font> holds  <font color="Olive" title="b3">a</font> is <a href="mssubfam.html#V5" title="MSSUBFAM:attr.5">properly-upper-bound</a>
 
;<br/>
<b>hence </b><a NAME="E4:61_1_1"/>
the <a href="closure1.html#U1" title="CLOSURE1:sel.1">Family</a> of <font color="Maroon" title="c2">CS</font> is <a href="mssubfam.html#V5" title="MSSUBFAM:attr.5">properly-upper-bound</a>
 <b>by </b><i><a class="txt" href="closure1.html#E2:61_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D10" target="_self" title="CLOSURE1:def.10">CLOSURE1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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