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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">B</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">B</font></span>)</span>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">B</font></span>)</span>;<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">x1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">A1</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x1</font>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> )
 ;<br/>

<a NAME="E3:13"/><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">B</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:13"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:13"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A1</font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D1" target="_self">Def1</a>, </i>;<br/>
<a NAME="E6:13"/><b>then </b>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D2" target="_self">Def2</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:13"/>
<font color="Maroon">A</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font>
 <b>by </b><i>, , </i>;<br/>


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