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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="membered.html#V2">real-membered</a> <a href="seq_4.html#V1">bounded_above</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be  <a href="rcomp_1.html#V2">closed</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="seq_4.html#V1">bounded_above</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="membered.html#T2">MEMBERED:2</a></i>;<br/>
<a NAME="E3:6"/><i><font color="Green">E34</font></i>: 
 <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="pscomp_1.html#T32">PSCOMP_1:32</a></i>;<br/>
<a NAME="E4:6"/><i><font color="Green">E35</font></i>: 
 <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="topreal6.html#T78">TOPREAL6:78</a></i>;<br/>
<a NAME="E5:6"/>
 <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T30">RCOMP_1:30</a></i>;<br/>
<b>hence </b><a NAME="E6:6"/>
 <a href="pscomp_1.html#NK2" target="_self">sup</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, </i>;<br/>


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