<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="membered.html#V2">real-membered</a> <a href="seq_4.html#V2">bounded_below</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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="E1:5"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="seq_4.html#V2">bounded_below</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="E3:5"/><i><font color="Green">E4</font></i>: 
 <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:5"><i><font color="Green">E3</font></i></a>, <a class="ref" href="pscomp_1.html#T32">PSCOMP_1:32</a></i>;<br/>
<a NAME="E4:5"/><i><font color="Green">E5</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <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">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="topreal6.html#T77">TOPREAL6:77</a></i>;<br/>
<a NAME="E5:5"/>
 <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">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T31">RCOMP_1:31</a></i>;<br/>
<b>hence </b><a NAME="E6:5"/>
 <a href="pscomp_1.html#NK3" target="_self">inf</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:5"><i><font color="Green">E4</font></i></a>, <a class="txt" href="rcomp_3.html#E4:5"><i><font color="Green">E5</font></i></a></i>;<br/>


</div>
