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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">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>





<a NAME="E1:4"/>
( <font color="Maroon">A</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> &amp; <font color="Maroon">B</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> iff ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E2:4"/><b>then </b>
( ( <font color="Maroon">A</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> &amp; <font color="Maroon">B</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> ) iff <font color="Maroon">x</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">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:4"/><b>then </b>
( ( <font color="Maroon">A</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> &amp; <font color="Maroon">B</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> ) iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="tops_1.html#T46">TOPS_1:46</a></i>;<br/>
<b>hence </b><a NAME="E4:4"/>
( ( <font color="Maroon">A</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> &amp; <font color="Maroon">B</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> ) iff <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> is    <a href="connsp_2.html#M1" target="_self">a_neighborhood</a> of <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/>


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