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<b>let </b><font color="Maroon">X</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</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>assume </b><a NAME="E1:11"/>
<font color="Maroon">B</font> is <a href="tops_1.html#V2">boundary</a>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E13</font></i>: 
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="tops_1.html#T84">TOPS_1:84</a></i>;<br/>
<b>assume </b><a NAME="E3:11"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 ;<br/>

<a NAME="E4:11"/><b>then </b>
 <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="ref" href="tops_1.html#T48">TOPS_1:48</a></i>;<br/>
<a NAME="E5:11"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="tops_3.html#T3" target="_self">Th3</a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<b>hence </b><a NAME="E6:11"/>
<font color="Maroon">A</font> is <a href="tops_1.html#V2">boundary</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T84">TOPS_1:84</a></i>;<br/>


</div>
