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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">X0</font> be  non <a href="struct_0.html#V3">empty</a> <a href="tsep_1.html#V1">open</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>





<b>reconsider </b><font color="Maroon">A0</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</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">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>assume </b><a NAME="E3:46"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">X0</font> <a href="tsep_1.html#NR2" target="_self">meets</a> <font color="Maroon">X1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">A0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X1</font> <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E5:46"/>
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A0</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X1</font></span>)</span> &amp; <font color="Maroon">A0</font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="tsep_1.html#T16">TSEP_1:16</a></i>;<br/>
<a NAME="E6:46"/><b>then </b>
( <font color="Maroon">B</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X0</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X1</font></span>)</span> &amp; <font color="Maroon">X0</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X1</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font> )
 
<b>by </b><i>, <a class="ref" href="tops_2.html#T32">TOPS_2:32</a>, <a class="ref" href="tsep_1.html#T30">TSEP_1:30</a>, <a class="ref" href="tsep_1.html#D5">TSEP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:46"/>
<font color="Maroon">X0</font> <a href="tsep_1.html#K2">meet</a> <font color="Maroon">X1</font> is  <a href="tsep_1.html#V1">open</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X1</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T16">TSEP_1:16</a></i>;<br/>


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