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<b>let </b><font color="Maroon" title="c1">S</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">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies <font color="Maroon" title="c1">S</font> is <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</a> )</span><br/>

<b>assume </b><a NAME="E1:24_1_1"/>
<font color="Maroon" title="c1">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">S</font> is <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</a></span><br/>

<a NAME="E2:24_1_1"/><b>then </b>
<font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K1" title="MEASURE5:func.1">].</a><span class="default"><a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a> ,<a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a> </span><a href="measure5.html#K1" title="MEASURE5:func.1">.[</a></span>
 
;<br/>
<a NAME="E3:24_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K1" title="MEASURE5:func.1">].</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="measure5.html#K1" title="MEASURE5:func.1">.[</a></span> )
 
;<br/>
<b>hence </b><a NAME="E4:24_1_1"/>
<font color="Maroon" title="c1">S</font> is <a href="measure5.html#V1" title="MEASURE5:attr.1">open_interval</a>
 <b>by </b><i><a class="ref" href="measure5.html#D5" target="_self" title="MEASURE5:def.5">Def5</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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