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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E15</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="tops_3.html#D3" target="_self">TOPS_3:def 3</a><br/>

<b>assume </b><a NAME="E2:25"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V1">dense</a>
 ;<br/>

<a NAME="E3:25"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tops_1.html#D3">TOPS_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:25"/>
contradiction
 <b>by </b><i><a class="txt" href="tops_3.html#E1:25"><i><font color="Green">E15</font></i></a>, <a class="ref" href="tops_1.html#T43">TOPS_1:43</a></i>;<br/>


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