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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="integra1.html#V1" title="INTEGRA1:attr.1">closed-interval</a> <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> ;<br/><b>let </b><font color="Maroon" title="c2">D2</font>, <font color="Maroon" title="c3">MD2</font> be    <a href="integra1.html#M3" title="INTEGRA1:mode.3">Element</a> of  <a href="integra1.html#K8" title="INTEGRA1:func.8">divs</a> <font color="Maroon" title="c1">A</font>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c3">MD2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c2">D2</font>
 ;<br/>

<a NAME="E2:23"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">MD2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E3:23"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">MD2</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T34" title="FINSEQ_3:th.34">FINSEQ_3:34</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
(  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <span class="p1">(<span class="default"><a href="integra1.html#K2" title="INTEGRA1:func.2">divset</a> <font color="Maroon" title="c3">MD2</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="integra1.html#K2" title="INTEGRA1:func.2">divset</a> <font color="Maroon" title="c3">MD2</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">MD2</font> <a href="goboard1.html#K1" title="GOBOARD1:func.1">.</a> 1 )
 
<b>by </b><i><a class="ref" href="integra1.html#D5" title="INTEGRA1:def.5">INTEGRA1:def 5</a></i>;<br/>
<b>then </b> <a href="integra1.html#K3" title="INTEGRA1:func.3">vol</a> <span class="p1">(<span class="default"><a href="integra1.html#K2" title="INTEGRA1:func.2">divset</a> <font color="Maroon" title="c3">MD2</font>,1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">MD2</font> <a href="goboard1.html#K1" title="GOBOARD1:func.1">.</a> 1</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="ref" href="integra1.html#D6" title="INTEGRA1:def.6">INTEGRA1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="txt" href="integra3.html#E1:23"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="finseq_1.html#T58" title="FINSEQ_1:th.58">FINSEQ_1:58</a></i>
;<br/>
<b>hence </b><a NAME="E6:23"/>
 <a href="integra1.html#K3" title="INTEGRA1:func.3">vol</a> <span class="p1">(<span class="default"><a href="integra1.html#K2" title="INTEGRA1:func.2">divset</a> <font color="Maroon" title="c3">MD2</font>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>


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