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<b>let </b><font color="Maroon">A</font> be  <a href="rcomp_1.html#V1">compact</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">B</font> be  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> ;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:4"/>
<font color="Maroon">A</font> is <a href="seq_4.html#V3">bounded</a>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T28">RCOMP_1:28</a></i>;<br/>
<a NAME="E3:4"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">A</font> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="seq_4.html#D3">SEQ_4:def 3</a></i>;<br/>
<a NAME="E4:4"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">B</font> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T3">RCOMP_1:3</a></i>;<br/>
<a NAME="E5:4"/>
<font color="Maroon">A</font> is <a href="rcomp_1.html#V2">closed</a>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T26">RCOMP_1:26</a></i>;<br/>
<a NAME="E6:4"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#T32">PSCOMP_1:32</a></i>;<br/>
<a NAME="E7:4"/><b>then </b>
 <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">B</font> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T3">RCOMP_1:3</a></i>;<br/>
<a NAME="E8:4"/><b>then </b>
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T31">RCOMP_1:31</a></i>;<br/>
<a NAME="E9:4"/><b>then </b>
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E10:4"/>
 <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="topreal6.html#T77">TOPREAL6:77</a></i>;<br/>


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