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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> is <a href="integra1.html#V1" title="INTEGRA1:attr.1">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/>

<b>assume </b><a NAME="E1:7_1_1"/>
<font color="Maroon" title="c1">A</font> is <a href="integra1.html#V1" title="INTEGRA1:attr.1">closed-interval</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">A</font> is <a href="xxreal_2.html#V5" title="XXREAL_2:attr.5">bounded</a></span><br/>

<b>hence </b><a NAME="E2:7_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> )
 <b>by </b><i><a class="ref" href="integra1.html#T3" target="_self" title="INTEGRA1:th.3">Th3</a></i>; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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