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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  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">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="E1:59"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">C</font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>assume </b><a NAME="E2:59"/><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="E3:59"/><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="E4:59"/><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="E5:59"/><b>then </b><i><font color="Green">E27</font></i>: 
( <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> &amp;  <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, <a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/>
<a NAME="E6:59"/><b>then </b><i><font color="Green">E37</font></i>: 
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> &amp;  <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">D</font> =  <a href="tops_1.html#K1">Int</a> <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="E8:59"/>
<font color="Maroon">D</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_3.html#T27" target="_self">Th27</a>, <a class="ref" href="tops_3.html#T28" target="_self">Th28</a>, <a class="ref" href="tops_3.html#D4" target="_self">Def4</a>, <a class="ref" href="tsep_1.html#T9">TSEP_1:9</a></i>;<br/>
<a NAME="E9:59"/><b>then </b>
( <font color="Maroon">D</font> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> &amp;  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="txt" href="tops_3.html#E6:59"><i><font color="Green">E37</font></i></a>, <a class="ref" href="tops_3.html#T30" target="_self">Th30</a>, <a class="ref" href="tops_3.html#D3" target="_self">Def3</a>, <a class="ref" href="tops_1.html#T56">TOPS_1:56</a></i>;<br/>
<b>hence </b><a NAME="E10:59"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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