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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">A1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A2</font> be   <a href="struct_0.html#NM2">Subset</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="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">B1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/><b>let </b><font color="Maroon">B2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X0</font>;<br/>











<b>reconsider </b><font color="Maroon">A1'</font> = <font color="Maroon">A1</font>, <font color="Maroon">A2'</font> = <font color="Maroon">A2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> ;<br/>
<b>assume </b><a NAME="E2:26"/>
<font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A1</font>
 ;<br/>

<a NAME="E3:26"/><b>then </b><i><font color="Green">E12</font></i>: 
<font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">C1</font> = <font color="Maroon">B1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>assume </b><a NAME="E5:26"/>
<font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font>
 ;<br/>

<a NAME="E6:26"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">B2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">C2</font> = <font color="Maroon">B2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>assume </b><a NAME="E8:26"/>
<font color="Maroon">A1</font>,<font color="Maroon">A2</font> <a href="connsp_1.html#R1">are_separated</a> 
 ;<br/>

<a NAME="E9:26"/><b>then </b>
<font color="Maroon">C1</font>,<font color="Maroon">C2</font> <a href="connsp_1.html#R1">are_separated</a> 
 
<b>by </b><i><a class="ref" href="tsep_2.html#T6" target="_self">Th6</a>, <a class="ref" href="tsep_2.html#T8" target="_self">Th8</a>, <a class="ref" href="connsp_1.html#T8">CONNSP_1:8</a></i>;<br/>
<b>hence </b><a NAME="E10:26"/>
<font color="Maroon">B1</font>,<font color="Maroon">B2</font> <a href="connsp_1.html#R1">are_separated</a> 
 <b>by </b><i><a class="ref" href="tsep_2.html#T4" target="_self">Th4</a></i>;<br/>


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