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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="cantor_1.html#M1">Basis</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:41"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<a NAME="E2:41"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="cantor_1.html#K1">UniCl</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="yellow_9.html#T16">YELLOW_9:16</a></i>;<br/>
<a NAME="E3:41"/><i><font color="Green">E17</font></i>: 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="cantor_1.html#K1">UniCl</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="cantor_1.html#D2">CANTOR_1:def 2</a></i>;<br/>
<a NAME="E4:41"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D1">PRE_TOPC:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:41"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow12.html#E2:41"><i><font color="Green">E16</font></i></a>, <a class="txt" href="yellow12.html#E3:41"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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