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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="tdlat_3.html#V4" title="TDLAT_3:attr.4">extremally_disconnected</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="tdlat_1.html#K4" title="TDLAT_1:func.4">Domains_Lattice</a> <font color="Maroon" title="c1">Y</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="tdlat_1.html#K1" title="TDLAT_1:func.1">Domains_of</a> <font color="Maroon" title="c1">Y</font>;<br/>





<a NAME="E1:71"/><i><font color="Green" title="E38">A1</font></i>: 
 <a href="tdlat_1.html#K4" title="TDLAT_1:func.4">Domains_Lattice</a> <font color="Maroon" title="c1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="tdlat_1.html#K1" title="TDLAT_1:func.1">Domains_of</a> <font color="Maroon" title="c1">Y</font></span>)</span>,<span class="p1">(<span class="default"><a href="tdlat_1.html#NK3" title="TDLAT_1:NK.3">D-Union</a> <font color="Maroon" title="c1">Y</font></span>)</span>,<span class="p1">(<span class="default"><a href="tdlat_1.html#NK5" title="TDLAT_1:NK.5">D-Meet</a> <font color="Maroon" title="c1">Y</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="tdlat_1.html#D4" title="TDLAT_1:def.4">TDLAT_1:def 4</a></i>;<br/>
<b>assume </b><a NAME="E2:71"/><i><font color="Green" title="E39">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font> )
 ;<br/>

<b>hence </b><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">b</font> = 
<span class="p1">(<span class="default"><a href="tdlat_1.html#NK3" title="TDLAT_1:NK.3">D-Union</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>
<b>by </b><i><a class="txt" href="tdlat_3.html#E1:71"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c4">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">B</font>
<b>by </b><i><a class="ref" href="tdlat_3.html#T47" target="_self" title="TDLAT_3:th.47">Th47</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> = 
<span class="p1">(<span class="default"><a href="tdlat_1.html#NK5" title="TDLAT_1:NK.5">D-Meet</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>
<b>by </b><i><a class="txt" href="tdlat_3.html#E1:71"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="tdlat_3.html#E2:71"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c4">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">B</font>
<b>by </b><i><a class="ref" href="tdlat_3.html#T47" target="_self" title="TDLAT_3:th.47">Th47</a></i>
;<br/>


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