<?xml version="1.0"?>
<div class="add">

<a NAME="E1:63_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  is  <a href="measure5.html#V1" target="_self">open_interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="supinf_1.html#K3">REAL</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:63_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2" target="_self">].</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="measure5.html#K2" target="_self">.[</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="supinf_1.html#NM3">R_eal</a>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="supinf_1.html#NM3">R_eal</a><b> such that </b><br/><a NAME="E3:63_1_1_1_1"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E4:63_1_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="measure5.html#K2" target="_self">.[</a></span> )
 <b>by </b><i><a class="txt" href="measure5.html#E3:63_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="measure5.html#T13" target="_self">Th13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:63_1_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  is  <a href="measure5.html#V1" target="_self">open_interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="supinf_1.html#K3">REAL</a> 
 <b>by </b><i><a class="ref" href="measure5.html#D5" target="_self">Def5</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:63_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="measure5.html#NM1">Interval</a> st <font color="Olive">b<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


</div>
