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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="E1:4"/><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#V1">bounded_above</a> )
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:4"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">r</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> holds <br/><font color="Olive">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="seq_4.html#D1">SEQ_4:def 1</a></i>;<br/>
<a NAME="E4:4"/>
for <font color="Olive">r</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> holds <br/><font color="Olive">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:4"/>
<font color="Maroon">Y1</font> is <a href="seq_4.html#V1">bounded_above</a>
 <b>by </b><i><a class="ref" href="seq_4.html#D1">SEQ_4:def 1</a></i>;<br/>


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