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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <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="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st ( ( <font color="Olive" title="b1">A</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> &amp; <font color="Olive" title="b2">B</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> ) or ( <font color="Olive" title="b1">A</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp; <font color="Olive" title="b2">B</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> ) ) holds <br/><font color="Olive" title="b1">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <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="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( ( <font color="Maroon" title="c2">A</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> ) or ( <font color="Maroon" title="c2">A</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> ) ) implies <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">B</font> )</span><br/>





<b>assume </b><a NAME="E1:3"/>
( ( <font color="Maroon" title="c2">A</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> ) or ( <font color="Maroon" title="c2">A</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a> &amp; <font color="Maroon" title="c3">B</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">B</font></span><br/>

<a NAME="E2:3"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="tops_3.html#T17" title="TOPS_3:th.17">TOPS_3:17</a>, <a class="ref" href="tops_3.html#T45" title="TOPS_3:th.45">TOPS_3:45</a></i>;<br/>
<b>hence </b><a NAME="E3:3"/>
<font color="Maroon" title="c2">A</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</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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