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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="tdlat_1.html#K5" title="TDLAT_1:func.5">Closed_Domains_of</a> <font color="Maroon" title="c1">T</font> holds  <span class="p1">(<span class="default"><a href="tdlat_1.html#NK9" title="TDLAT_1:NK.9">CLD-Union</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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">T</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="tdlat_1.html#K5" title="TDLAT_1:func.5">Closed_Domains_of</a> <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="tdlat_1.html#NK9" title="TDLAT_1:NK.9">CLD-Union</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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">T</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><br/>



<a NAME="E1:38"/><i><font color="Green" title="E31">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">D</font> where <font color="Olive" title="b1">D</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> : <font color="Olive" title="b1">D</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> </span>}</span>  &amp; <font color="Maroon" title="c3">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">E</font> where <font color="Olive" title="b1">E</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> : <font color="Olive" title="b1">E</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> </span>}</span>  )
 
;<br/>
<b>then consider </b><font color="Maroon" title="c4">D</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E3:38"/><i><font color="Green" title="E32">A2</font></i>: 
( <font color="Maroon" title="c4">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">D</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c5">E</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E5:38"/><i><font color="Green" title="E33">A3</font></i>: 
( <font color="Maroon" title="c5">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c5">E</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> )
 <b>by </b><i><a class="txt" href="#E1:38"><i><font color="Green" title="E31">A1</font></i></a></i>;<br/>
<a NAME="E6:38"/>
<font color="Maroon" title="c4">D</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">E</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a>
 
<b>by </b><i><a class="txt" href="#E3:38"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="#E5:38"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="tops_1.html#T108" title="TOPS_1:th.108">TOPS_1:108</a></i>;<br/>
<a NAME="E7:38"/><b>then </b>
<font color="Maroon" title="c4">D</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">E</font> is <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T106" title="TOPS_1:th.106">TOPS_1:106</a></i>;<br/>
<a NAME="E8:38"/><b>then </b><i><font color="Green" title="E34">A4</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="txt" href="#E3:38"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="#E5:38"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="tops_1.html#D6" title="TOPS_1:def.6">TOPS_1:def 6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">A0</font> = <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c7">B0</font> = <font color="Maroon" title="c3">B</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="tdlat_1.html#K1" title="TDLAT_1:func.1">Domains_of</a> <font color="Maroon" title="c1">T</font> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="tdlat_1.html#NK9" title="TDLAT_1:NK.9">CLD-Union</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> = 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">B</font>
<b>by </b><i><a class="ref" href="tdlat_1.html#D6" target="_self" title="TDLAT_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">B0</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c7">B0</font></span>)</span>
<b>by </b><i><a class="txt" href="#E8:38"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
<br/>.= 
<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">T</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>
<b>by </b><i><a class="ref" href="tdlat_1.html#D2" target="_self" title="TDLAT_1:def.2">Def2</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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