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<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #);<br/>
<b>assume </b><a NAME="E1:9"/><i><font color="Green">E6</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) is <a href="connsp_1.html#V1">connected</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></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="E2:9"/><i><font color="Green">E7</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E3:9"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="connsp_1.html#R1">are_separated</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) ;<br/>
<i><font color="Green">E9</font></i>:  <a href="pre_topc.html#K2">[#]</a> <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) = 
the <a href="struct_0.html#U1">carrier</a> of <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #)

<br/>.= 
<font color="Maroon">c<sub>9</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E2:9"><i><font color="Green">E7</font></i></a></i>
;<br/>
<a NAME="E6:9"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="connsp_1.html#R1">are_separated</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E3:9"><i><font color="Green">E8</font></i></a>, <a class="ref" href="topalg_3.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E7:9"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) )
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:9"><i><font color="Green">E6</font></i></a>, <a class="txt" href="topalg_3.html#E5:9"><i><font color="Green">E9</font></i></a>, <a class="ref" href="connsp_1.html#D2">CONNSP_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:9"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>


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