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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">F</font> being   <a href="measure7.html#M1" title="MEASURE7:mode.1">Interval_Covering</a> of <font color="Maroon" title="c2">A</font> st <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure7.html#K6" title="MEASURE7:func.6">vol</a> <font color="Olive" title="b1">F</font>;<br/>
<b>consider </b><font color="Maroon" title="c3">D</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:25_1_1"/><i><font color="Green" title="E23">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:25_1_1"/>
 <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> 
 
;<br/>
<b>then consider </b><font color="Maroon" title="c4">F0</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> <b> such that </b><br/><a NAME="E5:25_1_1"/><i><font color="Green" title="E24">A2</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">F0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> ,<a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c4">F0</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Maroon" title="c4">F0</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a>  ) )
 <b>by </b><i><a class="ref" href="measure1.html#T40" title="MEASURE1:th.40">MEASURE1:40</a></i>;<br/>
<a NAME="E6:25_1_1"/><i><font color="Green" title="E25">A3</font></i>: 
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> ,<a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="measure5.html#K6" title="MEASURE5:func.6">{}</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T93" title="ZFMISC_1:th.93">ZFMISC_1:93</a></i>;<br/>
<a NAME="E7:25_1_1"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c4">F0</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">n</font> is   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>
 
<b>by </b><i><a class="txt" href="measure7.html#E5:25_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="measure6.html#T35" title="MEASURE6:th.35">MEASURE6:35</a>, <a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">F0</font> = <font color="Maroon" title="c4">F0</font> as    <a href="measure7.html#M1" title="MEASURE7:mode.1">Interval_Covering</a> of <font color="Maroon" title="c2">A</font> <b>by </b><i><a class="txt" href="measure7.html#E5:25_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="measure7.html#E6:25_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="measure7.html#D2" target="_self" title="MEASURE7:def.2">Def2</a></i>;<br/>
<a NAME="E9:25_1_1"/>
 <a href="measure7.html#K6" title="MEASURE7:func.6">vol</a> <font color="Maroon" title="c5">F0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font>
 
<b>by </b><i><a class="txt" href="measure7.html#E2:25_1_1"><i><font color="Green" title="E23">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:25_1_1"/>
not  <a href="measure7.html#K8" title="MEASURE7:func.8">Svc</a> <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="measure7.html#D8" target="_self" title="MEASURE7:def.8">Def8</a></i>;<br/>


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