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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>reconsider </b><font color="Maroon">Y1</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K2">.</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> </span>}</span>  as   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  <b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> 0 = 
 <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">Y1</font>
<b>by </b><i/>
<br/>.= 
 <a href="rinfsup1.html#K1" target="_self">sup</a> <font color="Maroon">seq</font>
<b>by </b><i><a class="ref" href="setlim_1.html#T9">SETLIM_1:9</a></i>
;<br/>
<b>hence </b><a NAME="E3:48"/>
( <font color="Maroon">seq</font> is <a href="seq_2.html#V1">bounded_above</a> implies <span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="rinfsup1.html#K1" target="_self">sup</a> <font color="Maroon">seq</font> )
 ;<br/>


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