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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>thus </b><a NAME="E1:76"/>
( <font color="Maroon" title="c1">X</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a> implies  <a href="tdlat_1.html#K4" title="TDLAT_1:func.4">Domains_Lattice</a> <font color="Maroon" title="c1">X</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1"/>
<font color="Maroon" title="c1">X</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a>
 ;<br/>

<a NAME="E2:76_1"/><b>then </b>
 <a href="tdlat_1.html#K4" title="TDLAT_1:func.4">Domains_Lattice</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdlat_1.html#K12" title="TDLAT_1:func.12">Open_Domains_Lattice</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="tdlat_3.html#T46" target="_self" title="TDLAT_3:th.46">Th46</a></i>;<br/>
<b>hence </b><a NAME="E3:76_1"/>
 <a href="tdlat_1.html#K4" title="TDLAT_1:func.4">Domains_Lattice</a> <font color="Maroon" title="c1">X</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>
 ;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:76"/>
 <a href="tdlat_1.html#K4" title="TDLAT_1:func.4">Domains_Lattice</a> <font color="Maroon" title="c1">X</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>
 ;<br/>

<b>hence </b><a NAME="E3:76"/>
<font color="Maroon" title="c1">X</font> is <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#T51" target="_self" title="TDLAT_3:th.51">Th51</a></i>;<br/>


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