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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">CS</font> is  <a href="closure1.html#V7" title="CLOSURE1:attr.7">absolutely-additive</a>  implies <font color="Maroon" title="c2">CS</font> is  <a href="closure1.html#V11" title="CLOSURE1:attr.11">properly-lower-bound</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:62_1_1"/>
<font color="Maroon" title="c2">CS</font> is  <a href="closure1.html#V7" title="CLOSURE1:attr.7">absolutely-additive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">CS</font> is  <a href="closure1.html#V11" title="CLOSURE1:attr.11">properly-lower-bound</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:62_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#V6" title="MSSUBFAM:attr.6">properly-lower-bound</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="closure1.html#D11" target="_self" title="CLOSURE1:def.11">CLOSURE1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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