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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="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="tdlat_1.html#K8">Closed_Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="tdlat_1.html#K5">Closed_Domains_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:100"/><i><font color="Green">E63</font></i>: 
 <a href="tdlat_1.html#K8">Closed_Domains_Lattice</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="tdlat_1.html#K5">Closed_Domains_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="tdlat_1.html#NK9" target="_self">CLD-Union</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="tdlat_1.html#NK11" target="_self">CLD-Meet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="tdlat_1.html#D8">TDLAT_1:def 8</a></i>;<br/>
<b>assume </b><a NAME="E2:100"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>hence </b><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="tdlat_1.html#NK9" target="_self">CLD-Union</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="tdlat_2.html#E1:100"><i><font color="Green">E63</font></i></a>, <a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="tdlat_1.html#D6">TDLAT_1:def 6</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="tdlat_1.html#NK11" target="_self">CLD-Meet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="tdlat_2.html#E1:100"><i><font color="Green">E63</font></i></a>, <a class="txt" href="tdlat_2.html#E2:100"><i><font color="Green">E64</font></i></a>, <a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tdlat_1.html#D7">TDLAT_1:def 7</a></i>
;<br/>


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