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<b>let </b><font color="Maroon">X</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">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>





<b>reconsider </b><font color="Maroon">A1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font></span>)</span> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E4:36"/>
( ( <font color="Maroon">X1</font> is <a href="tex_3.html#V2" target="_self">everywhere_dense</a> &amp; <font color="Maroon">X2</font> is <a href="tex_3.html#V1" target="_self">dense</a> ) or ( <font color="Maroon">X1</font> is <a href="tex_3.html#V1" target="_self">dense</a> &amp; <font color="Maroon">X2</font> is <a href="tex_3.html#V2" target="_self">everywhere_dense</a> ) )
 ;<br/>

<a NAME="E5:36"/><b>then </b><i><font color="Green">E16</font></i>: 
( ( <font color="Maroon">A1</font> is <a href="tops_3.html#V1">everywhere_dense</a> &amp; <font color="Maroon">A2</font> is <a href="tops_1.html#V1">dense</a> ) or ( <font color="Maroon">A1</font> is <a href="tops_1.html#V1">dense</a> &amp; <font color="Maroon">A2</font> is <a href="tops_3.html#V1">everywhere_dense</a> ) )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:36"/><b>then </b>
<font color="Maroon">A1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:36"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">X1</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X2</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#D3">TSEP_1:def 3</a></i>;<br/>
<a NAME="E8:36"/>
<font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i><a class="ref" href="tex_3.html#T1" target="_self">Th1</a>, <a class="ref" href="tops_3.html#T45">TOPS_3:45</a></i>;<br/>
<a NAME="E9:36"/><b>then </b>
<font color="Maroon">A</font> is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i><a class="txt" href="tex_3.html#E5:36"><i><font color="Green">E16</font></i></a>, <a class="ref" href="tsep_1.html#D5">TSEP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E10:36"/>
<font color="Maroon">X1</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X2</font> is  <a href="tex_3.html#V1" target="_self">dense</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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