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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">X1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">X2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</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">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span>;<br/><b>let </b><font color="Maroon">x1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X1</font>;<br/><b>let </b><font color="Maroon">x2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X2</font>;<br/>











<b>assume </b><a NAME="E1:22"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 ;<br/>

<b>let </b><font color="Maroon">A1</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">x1</font>;<br/><b>let </b><font color="Maroon">A2</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">x2</font>;<br/>



<b>consider </b><font color="Maroon">U1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X1</font><b> such that </b><br/><a NAME="E3:22"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">U1</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">U1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U1</font> )
 <b>by </b><i><a class="ref" href="connsp_2.html#T8">CONNSP_2:8</a></i>;<br/>
<b>consider </b><font color="Maroon">U2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X2</font><b> such that </b><br/><a NAME="E5:22"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">U2</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">U2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">U2</font> )
 <b>by </b><i><a class="ref" href="connsp_2.html#T8">CONNSP_2:8</a></i>;<br/>
<b>consider </b><font color="Maroon">V</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">X1</font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">X2</font></span>)</span><b> such that </b><br/><a NAME="E7:22"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">U1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">U2</font> )
 <b>by </b><i>, , <a class="ref" href="tmap_1.html#T2" target="_self">Th2</a>, <a class="ref" href="tmap_1.html#T1" target="_self">Th1</a></i>;<br/>
<b>take </b>
<font color="Maroon">V</font>
;<br/>

<a NAME="E8:22"/>
<font color="Maroon">U1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">U2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font>
 
<b>by </b><i>, <a class="ref" href="tmap_1.html#T2" target="_self">Th2</a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<b>hence </b><a NAME="E9:22"/>
( <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> )
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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