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<b>let </b><font color="Maroon">X1</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X2</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">D1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X1</font>;<br/><b>let </b><font color="Maroon">D2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X2</font>;<br/>







<b>assume </b><a NAME="E1:83"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">D1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D2</font>
 ;<br/>

<b>assume </b><a NAME="E2:83"/><i><font color="Green">E23</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X1</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X1</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X2</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X2</font> #)
 ;<br/>

<a NAME="E3:83"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">D1</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D1</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">C2</font> =  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D1</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X2</font> <b>by </b><i/>;<br/>
<a NAME="E5:83"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">D2</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D2</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">C1</font> =  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X1</font> <b>by </b><i/>;<br/>
<a NAME="E7:83"/>
( <font color="Maroon">C2</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">C1</font> is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:83"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C1</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C2</font> )
 
<b>by </b><i>, , , <a class="ref" href="tops_1.html#T31">TOPS_1:31</a></i>;<br/>
<b>hence </b><a NAME="E9:83"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D1</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">D2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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