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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="tdlat_3.html#V4" target="_self">extremally_disconnected</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<a NAME="E1:69"/>
(  <a href="tdlat_1.html#K1">Domains_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tdlat_1.html#K9">Open_Domains_of</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="tdlat_1.html#NK3" target="_self">D-Union</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tdlat_1.html#NK15" target="_self">OPD-Union</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="tdlat_1.html#NK5" target="_self">D-Meet</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tdlat_1.html#NK17" target="_self">OPD-Meet</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="tdlat_3.html#T44" target="_self">Th44</a>, <a class="ref" href="tdlat_3.html#T45" target="_self">Th45</a></i>;<br/>
<b>hence </b> <a href="tdlat_1.html#K4">Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="tdlat_1.html#K9">Open_Domains_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="tdlat_1.html#NK15" target="_self">OPD-Union</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="tdlat_1.html#NK17" target="_self">OPD-Meet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
<b>by </b><i><a class="ref" href="tdlat_1.html#D4">TDLAT_1:def 4</a></i>
<br/>.= 
 <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_1.html#D12">TDLAT_1:def 12</a></i>
;<br/><br/>


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