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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="measure6.html#K3" title="MEASURE6:func.3">--</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="E1:52"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure6.html#K3" title="MEASURE6:func.3">--</a> <span class="p1">(<span class="default"><a href="measure6.html#K3" title="MEASURE6:func.3">--</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E2:52"/>
( <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="measure6.html#K3" title="MEASURE6:func.3">--</a> <font color="Maroon" title="c1">X</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="measure6.html#E49"><span class="lab"><font color="Green" title="E19">Lm2</font></span></a>, <a class="txt" href="measure6.html#E50"><span class="lab"><font color="Green" title="E20">Lm3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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