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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Y</font> be  <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c2">Y</font> is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a>
 ;<br/>

<a NAME="E3:56"/>
for <font color="Olive" title="b1">t</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Olive" title="b1">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="seq_4.html#E1:56"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="seq_4.html#E2:56"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="seq_4.html#D4" target="_self" title="SEQ_4:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E4:56"/>
 <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <font color="Maroon" title="c1">X</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="seq_4.html#K2" title="SEQ_4:func.2">upper_bound</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="ref" href="seq_4.html#T62" target="_self" title="SEQ_4:th.62">Th62</a></i>;<br/>


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