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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM1" title="PROB_1:NM.1">Field_Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="measure1.html#M1" title="MEASURE1:mode.1">Measure</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c4">A</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c5">B</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c4">A</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="ref" href="measure1.html#T20" target="_self" title="MEASURE1:th.20">Th20</a></i>;<br/>
<a NAME="E3:23"/>
<font color="Maroon" title="c4">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c6">C</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
<font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c6">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="measure1.html#D5" target="_self" title="MEASURE1:def.5">Def5</a></i>;<br/>
<a NAME="E5:23"/><b>then </b><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c6">C</font></span>)</span>
 
<b>by </b><i><a class="txt" href="measure1.html#E1:23"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E6:23"/>
<font color="Maroon" title="c3">M</font> is <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>
 
<b>by </b><i><a class="ref" href="measure1.html#D5" target="_self" title="MEASURE1:def.5">Def5</a></i>;<br/>
<a NAME="E7:23"/><b>then </b>
(  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c4">A</font> &amp;  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c6">C</font> &amp; <font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c4">A</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  )
 
<b>by </b><i><a class="txt" href="measure1.html#E1:23"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="measure1.html#D4" target="_self" title="MEASURE1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:23"/>
<font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c4">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="measure1.html#E5:23"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="measure1.html#T5" target="_self" title="MEASURE1:th.5">Th5</a></i>;<br/>


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