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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <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="subset_1.html#M2">Element</a> of  <a href="tdlat_1.html#K9" target="_self">Open_Domains_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:50"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> is <a href="tops_1.html#V6">open_condensed</a> </span>}</span>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> is <a href="tops_1.html#V6">open_condensed</a> </span>}</span>  )
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:50"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="tops_1.html#V6">open_condensed</a> )
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:50"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="tops_1.html#V6">open_condensed</a> )
 <b>by </b><i><a class="txt" href="tdlat_1.html#E1:50"><i><font color="Green">E38</font></i></a></i>;<br/>
<a NAME="E6:50"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="txt" href="tdlat_1.html#E3:50"><i><font color="Green">E39</font></i></a>, <a class="txt" href="tdlat_1.html#E5:50"><i><font color="Green">E40</font></i></a>, <a class="ref" href="tops_1.html#T107">TOPS_1:107</a></i>;<br/>
<a NAME="E7:50"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T37">TOPS_1:37</a></i>;<br/>
<a NAME="E8:50"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <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="tops_1.html#T55">TOPS_1:55</a></i>;<br/>
<a NAME="E9:50"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<a NAME="E10:50"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="tdlat_1.html#E3:50"><i><font color="Green">E39</font></i></a>, <a class="txt" href="tdlat_1.html#E5:50"><i><font color="Green">E40</font></i></a>, <a class="txt" href="tdlat_1.html#E8:50"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tops_1.html#T48">TOPS_1:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="tdlat_1.html#K1" target="_self">Domains_of</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>thus </b><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> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> = 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tdlat_1.html#D10" target="_self">Def10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="tdlat_1.html#E10:50"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="tdlat_1.html#NK3" target="_self">D-Union</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="tdlat_1.html#D2" target="_self">Def2</a></i>
;<br/>


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