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<b>let </b><font color="Maroon">T</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">T</font>, <font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">B1</font> be    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">x</font>;<br/><b>let </b><font color="Maroon">B2</font> be    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">y</font>;<br/><b>let </b><font color="Maroon">U</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:12"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U</font> &amp; <font color="Maroon">U</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B2</font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b>
<font color="Maroon">U</font> is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="yellow_8.html#T21">YELLOW_8:21</a></i>;<br/>
<b>then consider </b><font color="Maroon">V</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:12"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">U</font> )
 <b>by </b><i>, <a class="ref" href="yellow_8.html#T22">YELLOW_8:22</a></i>;<br/>
<a NAME="E5:12"/>
<font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, <a class="ref" href="yellow_8.html#T21">YELLOW_8:21</a></i>;<br/>
<b>hence </b><a NAME="E6:12"/>
 ex <font color="Olive">V</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B1</font> &amp; <font color="Olive">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">U</font> )
 <b>by </b><i/>;<br/>


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