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<span class="kw">let </span><font color="Maroon" title="c1">IT</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"> ( <font color="Maroon" title="c1">IT</font> is  <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  implies <font color="Maroon" title="c1">IT</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:1_1_1"/>
<font color="Maroon" title="c1">IT</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">IT</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> </span><br/>

<a NAME="E2:1_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <font color="Maroon" title="c1">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure5.html#D3" title="MEASURE5:def.3">MEASURE5:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:1_1_1"/>
<font color="Maroon" title="c1">IT</font> is  <a href="rcomp_1.html#V1" title="RCOMP_1:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rcomp_1.html#T6" title="RCOMP_1:th.6">RCOMP_1:6</a></span>; <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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