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

<b>let </b><font color="Maroon">A</font> be  <a href="integra1.html#V1">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">D2</font> be    <a href="integra1.html#M3">Element</a> of  <a href="integra1.html#K8">divs</a> <font color="Maroon">A</font>, <font color="Maroon">MD2</font> be    <a href="integra1.html#M3">Element</a> of  <a href="integra1.html#K8">divs</a> <font color="Maroon">A</font>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">MD2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <font color="Maroon">A</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">D2</font>
 ;<br/>

<a NAME="E2:23"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">MD2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<a NAME="E3:23"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">MD2</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T34">FINSEQ_3:34</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
(  <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><a href="integra1.html#K2">divset</a> <font color="Maroon">MD2</font>,1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">A</font> &amp;  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="integra1.html#K2">divset</a> <font color="Maroon">MD2</font>,1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">MD2</font> <a href="goboard1.html#K1">.</a> 1 )
 
<b>by </b><i><a class="ref" href="integra1.html#D5">INTEGRA1:def 5</a></i>;<br/>
<b>then </b> <a href="integra1.html#K3">vol</a> <span class="p1">(<span class="default"><a href="integra1.html#K2">divset</a> <font color="Maroon">MD2</font>,1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">MD2</font> <a href="goboard1.html#K1">.</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <font color="Maroon">A</font></span>)</span>
<b>by </b><i><a class="ref" href="integra1.html#D6">INTEGRA1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <font color="Maroon">A</font></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>
;<br/>
<b>hence </b><a NAME="E6:23"/>
 <a href="integra1.html#K3">vol</a> <span class="p1">(<span class="default"><a href="integra1.html#K2">divset</a> <font color="Maroon">MD2</font>,1</span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>


</div>
