<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>thus </b><a NAME="E1:76"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="tdlat_3.html#V4" target="_self">extremally_disconnected</a> implies  <a href="tdlat_1.html#K4">Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM8">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">c<sub>1</sub></font> is <a href="tdlat_3.html#V4" target="_self">extremally_disconnected</a>
 ;<br/>

<a NAME="E2:76_1"/><b>then </b>
 <a href="tdlat_1.html#K4">Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tdlat_1.html#K12">Open_Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tdlat_3.html#T46" target="_self">Th46</a></i>;<br/>
<b>hence </b><a NAME="E3:76_1"/>
 <a href="tdlat_1.html#K4">Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM8">B_Lattice</a>
 ;<br/>


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

<b>assume </b><a NAME="E2:76"/>
 <a href="tdlat_1.html#K4">Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM8">B_Lattice</a>
 ;<br/>

<b>hence </b><a NAME="E3:76"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="tdlat_3.html#V4" target="_self">extremally_disconnected</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#T51" target="_self">Th51</a></i>;<br/>


</div>
