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<a NAME="E1:12_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">M</font>
 
;<br/>
<a NAME="E2:12_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="compl_sp.html#V3" title="COMPL_SP:attr.3">closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compl_sp.html#D4" target="_self" title="COMPL_SP:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:12_2_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font> st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="compl_sp.html#V3" title="COMPL_SP:attr.3">closed</a>  &amp; not <font color="Olive">b<sub>1</sub></font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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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