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<b>let </b><font color="Maroon" title="c6">S</font>, <font color="Maroon" title="c7">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c8">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">S</font>;<br/><b>let </b><font color="Maroon" title="c9">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">T</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green" title="E16">A1</font></i>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">S</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c6">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">T</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">T</font> #)
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c8">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">B</font>
 <b>and </b><br/><a NAME="E3:9"/><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c8">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">P</font>, <font color="Maroon" title="c11">Q</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">T</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:9_1"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c9">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">Q</font>
 <b>and </b><br/><a NAME="E2:9_1"/><i><font color="Green" title="E20">A5</font></i>: 
<font color="Maroon" title="c10">P</font>,<font color="Maroon" title="c11">Q</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 ;<br/><b>reconsider </b><font color="Maroon" title="c12">P1</font> = <font color="Maroon" title="c10">P</font>, <font color="Maroon" title="c13">Q1</font> = <font color="Maroon" title="c11">Q</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">S</font> <b>by </b><i><a class="txt" href="topalg_5.html#E1:9"><i><font color="Green" title="E16">A1</font></i></a></i>;<br/><a NAME="E4:9_1"/>
<font color="Maroon" title="c12">P1</font>,<font color="Maroon" title="c13">Q1</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 <b>by </b><i><a class="txt" href="topalg_5.html#E1:9"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="topalg_5.html#E2:9_1"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="topalg_5.html#T5" target="_self" title="TOPALG_5:th.5">Th5</a></i>;<br/><a NAME="E5:9_1"/><b>then </b>
( <font color="Maroon" title="c12">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c6">S</font> or <font color="Maroon" title="c13">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c6">S</font> )
 <b>by </b><i><a class="txt" href="topalg_5.html#E2:9"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="topalg_5.html#E3:9"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="topalg_5.html#E1:9_1"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="connsp_1.html#T16" title="CONNSP_1:th.16">CONNSP_1:16</a></i>;<br/><b>hence </b><a NAME="E6:9_1"/>
( <font color="Maroon" title="c10">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c7">T</font> or <font color="Maroon" title="c11">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c7">T</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon" title="c9">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#T16" title="CONNSP_1:th.16">CONNSP_1:16</a></i>;<br/>


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