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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">X0</font> be  non <a href="struct_0.html#V3">empty</a> <a href="tsep_1.html#V1">open</a>  <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">X0</font>;<br/>







<b>assume </b><a NAME="E1:69"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">C</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E3:69"/>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> is <a href="pre_topc.html#V3">open</a> )
 
<b>by </b><i><a class="ref" href="tops_3.html#T32" target="_self">Th32</a>, <a class="ref" href="tsep_1.html#D1">TSEP_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:69"/>
( <font color="Maroon">A</font> is <a href="tops_1.html#V2">boundary</a> iff <font color="Maroon">B</font> is <a href="tops_1.html#V2">boundary</a> )
 <b>by </b><i><a class="ref" href="tops_3.html#T32" target="_self">Th32</a>, <a class="ref" href="tops_3.html#T30" target="_self">Th30</a>, <a class="ref" href="tops_3.html#D4" target="_self">Def4</a></i>;<br/>


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