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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="pre_topc.html#K1">{}</a> <a href="topmetr.html#K3">R^1</a>  as   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a>  ;<br/>
<b>assume </b><a NAME="E2:112"/>
 <a href="numbers.html#K1">REAL</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a> 
 ;<br/>

<a NAME="E3:112"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <a href="topmetr.html#K3">R^1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<a NAME="E4:112"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a> 
 
;<br/>
<a NAME="E5:112"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> 
 
;<br/>
<b>hence </b><a NAME="E6:112"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>


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