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<b>let </b><font color="Maroon">c<sub>1</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>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:33_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="topgen_1.html#V1" target="_self">isolated</a>
 ;<br/><a NAME="E2:33_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="topgen_1.html#R2" target="_self">is_isolated_in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="topgen_1.html#D5" target="_self">Def5</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:33_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="topgen_1.html#T24" target="_self">Th24</a></i>;<br/><b>thus </b><a NAME="E5:33_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a>, <a class="txt" href="topgen_1.html#E4:33_1"><i><font color="Green">E20</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:33"/><i><font color="Green">E20</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<a NAME="E3:33"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E4:33"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="topgen_1.html#R2" target="_self">is_isolated_in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E2:33"><i><font color="Green">E20</font></i></a>, <a class="ref" href="topgen_1.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E5:33"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="topgen_1.html#V1" target="_self">isolated</a>
 <b>by </b><i><a class="ref" href="topgen_1.html#D5" target="_self">Def5</a></i>;<br/>


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