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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="integra1.html#V1">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:24"/>
<font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#R1">is_bounded_above_on</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:24"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> is <a href="seq_4.html#V1">bounded_above</a>
 
<b>by </b><i><a class="ref" href="integra1.html#T15">INTEGRA1:15</a></i>;<br/>
<a NAME="E3:24"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T99">RELAT_1:99</a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="seq_4.html#V1">bounded_above</a>
 <b>by </b><i><a class="txt" href="integra4.html#E2:24"><i><font color="Green">E24</font></i></a>, <a class="ref" href="rcomp_1.html#T4">RCOMP_1:4</a></i>;<br/>


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