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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:36"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V1">bounded_above</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E2:36"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E3:36"/>
<font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="seq_2.html#V1">bounded_above</a>
 
<b>by </b><i><a class="txt" href="rinfsup1.html#E1:36"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rinfsup1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E4:36"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seqm_3.html#K1">^\</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="ref" href="rinfsup1.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="seq_4.html#V1">bounded_above</a>
 <b>by </b><i><a class="txt" href="rinfsup1.html#E2:36"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rinfsup1.html#T30" target="_self">Th30</a></i>;<br/>


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