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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#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> holds <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">Y</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> <font color="Olive" title="b1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">B</font> &amp; <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#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> <font color="Olive" title="b1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b2">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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#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> <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">B</font> &amp; <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#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> <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">B</font> )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c4">A0</font> = <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c5">B0</font> = <font color="Maroon" title="c3">B</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="tdlat_1.html#K5" title="TDLAT_1:func.5">Closed_Domains_of</a> <font color="Maroon" title="c1">Y</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#T41" target="_self" title="TDLAT_3:th.41">Th41</a></span>;<br/>
<a NAME="E2:72"/>
<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#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#NK9" title="TDLAT_1:NK.9">CLD-Union</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">A0</font>,<font color="Maroon" title="c5">B0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#T42" target="_self" title="TDLAT_3:th.42">Th42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:72"/>
<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#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> <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_1.html#D6" title="TDLAT_1:def.6">TDLAT_1:def 6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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#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> <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">B</font></span><br/>

<span class="kw">reconsider </span><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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="tdlat_1.html#K9" title="TDLAT_1:func.9">Open_Domains_of</a> <font color="Maroon" title="c1">Y</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#T44" target="_self" title="TDLAT_3:th.44">Th44</a></span>;<br/>
<a NAME="E5:72"/>
<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#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#NK17" title="TDLAT_1:NK.17">OPD-Meet</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c6">A0</font>,<font color="Maroon" title="c7">B0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_3.html#T45" target="_self" title="TDLAT_3:th.45">Th45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:72"/>
<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#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> <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tdlat_1.html#D11" title="TDLAT_1:def.11">TDLAT_1:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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