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<a NAME="E1:75"/><i><font color="Green" title="E53">A</font></i>: 
 <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  is    <a href="xxreal_2.html#M1" title="XXREAL_2:mode.1">UpperBound</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xxreal_2.html#T37" target="_self" title="XXREAL_2:th.37">TW2</a></i>;<br/>
<a NAME="E2:75"/>
for <font color="Olive" title="b1">x</font> being   <a href="xxreal_2.html#M1" title="XXREAL_2:mode.1">UpperBound</a> of  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds   <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">x</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T5" title="XXREAL_0:th.5">XXREAL_0:5</a></i>;<br/>
<b>hence </b><a NAME="E3:75"/>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a> 
 <b>by </b><i><a class="txt" href="#E1:75"><i><font color="Green" title="E53">A</font></i></a>, <a class="ref" href="xxreal_2.html#D3" target="_self" title="XXREAL_2:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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