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<b>let </b><font color="Maroon" title="c1">X</font> be  <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</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>let </b><font color="Maroon" title="c2">X'</font> be   <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> ;<br/>



<b>assume </b><a NAME="E1:113"/>
<font color="Maroon" title="c2">X'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 ;<br/>

<a NAME="E2:113"/><b>then </b>
<font color="Maroon" title="c2">X'</font> is <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>
 
<b>by </b><i><a class="ref" href="topreal6.html#T81" title="TOPREAL6:th.81">TOPREAL6:81</a></i>;<br/>
<a NAME="E3:113"/><b>then </b>
<font color="Maroon" title="c2">X'</font> is <a href="seq_4.html#V3" title="SEQ_4:attr.3">bounded</a>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T28" title="RCOMP_1:th.28">RCOMP_1:28</a></i>;<br/>
<b>hence </b><a NAME="E4:113"/>
( <font color="Maroon" title="c2">X'</font> is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a> &amp; <font color="Maroon" title="c2">X'</font> is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a> )
 <b>by </b><i><a class="ref" href="seq_4.html#D3" title="SEQ_4:def.3">SEQ_4:def 3</a></i>;<br/>


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