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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c2">X</font> = <font color="Maroon" title="c1">A</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">X</font>
;<br/>

 <a href="weierstr.html#K5" title="WEIERSTR:func.5">lower_bound</a> <font color="Maroon" title="c1">A</font> = 
 <a href="seq_4.html#K5" title="SEQ_4:func.5">lower_bound</a> <span class="p1">(<span class="default"><a href="weierstr.html#K3" title="WEIERSTR:func.3">[#]</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="ref" href="weierstr.html#D5" title="WEIERSTR:def.5">WEIERSTR:def 5</a></i>
<br/>.= 
 <a href="seq_4.html#K5" title="SEQ_4:func.5">lower_bound</a> <font color="Maroon" title="c2">X</font>
<b>by </b><i><a class="ref" href="weierstr.html#D3" title="WEIERSTR:def.3">WEIERSTR:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E3:11"/>
( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> &amp;  <a href="weierstr.html#K5" title="WEIERSTR:func.5">lower_bound</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#NK3" title="PSCOMP_1:NK.3">inf</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>


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