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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">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="E1:55"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">D</font> = <font color="Maroon">B</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E3:55"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D</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="pre_topc.html#T47">PRE_TOPC:47</a></i>;<br/>
<a NAME="E4:55"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="tops_3.html#T18" target="_self">Th18</a>, <a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E5:55"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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