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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="t_0topsp.html#V2">V118</a>  <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">X</font>, <font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="t_0topsp.html#V2">V118</a>  <a href="tsp_1.html#M2" target="_self">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>, <font color="Maroon">A2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font> as  non <a href="xboole_0.html#V1">empty</a> <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="E2:41"/>
( <font color="Maroon">X1</font> is <a href="tsep_1.html#V1">open</a> or <font color="Maroon">X2</font> is <a href="tsep_1.html#V1">open</a> )
 ;<br/>

<a NAME="E3:41"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">A1</font> is <a href="pre_topc.html#V3">open</a> or <font color="Maroon">A2</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="E4:41"/><i><font color="Green">E18</font></i>: 
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#K1">union</a> <font color="Maroon">X2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#D2">TSEP_1:def 2</a></i>;<br/>
<a NAME="E5:41"/>
( <font color="Maroon">A1</font> is <a href="tsp_1.html#V1" target="_self">T_0</a> &amp; <font color="Maroon">A2</font> is <a href="tsp_1.html#V1" target="_self">T_0</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:41"/><b>then </b>
<font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> is <a href="tsp_1.html#V1" target="_self">T_0</a>
 
<b>by </b><i>, <a class="txt" href="tsp_1.html#E3:41"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:41"/>
<font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font> is <a href="t_0topsp.html#V2">T_0</a>
 <b>by </b><i>, </i>;<br/>


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