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<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></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">c<sub>8</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>6</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="connsp_2.html#M2">a_neighborhood</a> of <font color="Maroon">c<sub>8</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:12"/><i><font color="Green">E17</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>6</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>6</sub></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">c<sub>7</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>7</sub></font> #)
 <b>and </b><br/><a NAME="E2:12"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>7</sub></font> <b>by </b><i><a class="txt" href="topalg_5.html#E1:12"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E4:12"/><i><font color="Green">E19</font></i>: 
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="topalg_5.html#E1:12"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tops_3.html#T77">TOPS_3:77</a></i>;<br/>
<a NAME="E5:12"/>
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D2">CONNSP_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:12"/>
<font color="Maroon">c<sub>10</sub></font> is    <a href="connsp_2.html#M2">a_neighborhood</a> of <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="topalg_5.html#E2:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="topalg_5.html#E4:12"><i><font color="Green">E19</font></i></a>, <a class="ref" href="connsp_2.html#D2">CONNSP_2:def 2</a></i>;<br/>


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