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<b>let </b><font color="Maroon" title="c3">SF</font> be   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c2">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">SF</font> is <a href="mssubfam.html#V2" title="MSSUBFAM:attr.2">absolutely-additive</a> implies <font color="Maroon" title="c3">SF</font> is <a href="mssubfam.html#V6" title="MSSUBFAM:attr.6">properly-lower-bound</a> )</span><br/>

<b>assume </b><a NAME="E1:85_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c3">SF</font> is <a href="mssubfam.html#V2" title="MSSUBFAM:attr.2">absolutely-additive</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">SF</font> is <a href="mssubfam.html#V6" title="MSSUBFAM:attr.6">properly-lower-bound</a></span><br/>

<a NAME="E2:85_1_1"/>
 <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Maroon" title="c2">M</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T49" title="PBOOLE:th.49">PBOOLE:49</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">a</font> =  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> as   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c2">M</font> <b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E4:85_1_1"/><i><font color="Green" title="E21">A2</font></i>: 
 <a href="mboolean.html#K2" title="MBOOLEAN:func.2">union</a> <font color="Maroon" title="c4">a</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="mboolean.html#T22" title="MBOOLEAN:th.22">MBOOLEAN:22</a></i>;<br/>
<a NAME="E5:85_1_1"/>
 <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">SF</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T49" title="PBOOLE:th.49">PBOOLE:49</a></i>;<br/>
<b>hence </b><a NAME="E6:85_1_1"/>
 <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c3">SF</font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E1:85_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="mssubfam.html#E4:85_1_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="mssubfam.html#D4" target="_self" title="MSSUBFAM:def.4">Def4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="mssubfam.html#D8" target="_self" title="MSSUBFAM:def.8">MSSUBFAM:def 8</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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