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<b>let </b><font color="Maroon">Y1</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">Y</font> be   <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">E41</font></i>: 
( <font color="Maroon">Y1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> is <a href="seq_4.html#V3">bounded</a> )
 ;<br/>

<a NAME="E2:5"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">Y</font> is <a href="seq_4.html#V1">bounded_above</a> &amp; <font color="Maroon">Y</font> is <a href="seq_4.html#V2">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="seq_4.html#D3">SEQ_4:def 3</a></i>;<br/>
<a NAME="E3:5"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">Y1</font> is <a href="seq_4.html#V1">bounded_above</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:5"/>
<font color="Maroon">Y1</font> is <a href="seq_4.html#V2">bounded_below</a>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:5"/>
<font color="Maroon">Y1</font> is <a href="seq_4.html#V3">bounded</a>
 <b>by </b><i>, <a class="ref" href="seq_4.html#D3">SEQ_4:def 3</a></i>;<br/>


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