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<b>let </b><font color="Maroon">S</font> be   <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green">E72</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #)
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">S</font> is <a href="connsp_1.html#V1">connected</a>
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_1.html#D2">CONNSP_1:def 2</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:9"/><i><font color="Green">E75</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E4:9"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="connsp_1.html#R1">are_separated</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">A1</font> = <font color="Maroon">A</font>, <font color="Maroon">B1</font> = <font color="Maroon">B</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<a NAME="E6:9"/><i><font color="Green">E79</font></i>: 
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp;  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> )
 
;<br/>
<a NAME="E7:9"/>
<font color="Maroon">A1</font>,<font color="Maroon">B1</font> <a href="connsp_1.html#R1">are_separated</a> 
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E8:9"/><b>then </b>
( <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">S</font> or <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">S</font> )
 
<b>by </b><i>, , , , <a class="ref" href="connsp_1.html#D2">CONNSP_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E9:9"/>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> or <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> )
 ;<br/>


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