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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> iff  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> )</span><br/>

<a NAME="E1:24"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E2:24"/>
( <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a> iff  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">-</a> <font color="Maroon" title="c1">X</font> is <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a> )
 <b>by </b><i><a class="txt" href="pscomp_1.html#E22"><i><font color="Green" title="E14">Lm1</font></i></a>, <a class="txt" href="pscomp_1.html#E23"><i><font color="Green" title="E15">Lm2</font></i></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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