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<span class="kw">let </span><font color="Maroon" title="c1">A</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  implies <font color="Maroon" title="c1">A</font> is  <a href="xxreal_2.html#V5" title="XXREAL_2:attr.5">bounded</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:5_1_1"/>
(  not <font color="Maroon" title="c1">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c1">A</font> is  <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">A</font> is  <a href="xxreal_2.html#V5" title="XXREAL_2:attr.5">bounded</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:5_1_1"/>
( <font color="Maroon" title="c1">A</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>  &amp; <font color="Maroon" title="c1">A</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="integra1.html#T3" target="_self" title="INTEGRA1:th.3">Th3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xxreal_2.html#D11" title="XXREAL_2:def.11">XXREAL_2:def 11</a> <a class="txt" 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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