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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">Y0</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y0</font>;<br/>







<b>assume </b><a NAME="E1:56"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">C</font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>

<b>assume </b><a NAME="E2:56"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 ;<br/>

<b>assume </b><a NAME="E3:56"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 ;<br/>

<b>assume </b><a NAME="E4:56"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E5:56"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="tops_3.html#T27" target="_self">Th27</a>, <a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a></i>;<br/>
<a NAME="E6:56"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="tops_3.html#D3" target="_self">Def3</a>, <a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<a NAME="E7:56"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 
<b>by </b><i><a class="ref" href="tops_3.html#T26" target="_self">Th26</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:56"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y0</font>
 
;<br/>
<a NAME="E9:56"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">Y0</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E10:56"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="tops_3.html#T28" target="_self">Th28</a>, <a class="ref" href="pre_topc.html#T47">PRE_TOPC:47</a></i>;<br/>


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