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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <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> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

 <a href="weierstr.html#K4">upper_bound</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="seq_4.html#K4">upper_bound</a> <span class="p1">(<span class="default"><a href="weierstr.html#K3">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="weierstr.html#D4">WEIERSTR:def 4</a></i>
<br/>.= 
 <a href="seq_4.html#K4">upper_bound</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="weierstr.html#D3">WEIERSTR:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E3:12"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="weierstr.html#K4">upper_bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#NK2" target="_self">sup</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


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