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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM1">Field_Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="measure1.html#M1" target="_self">Measure</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">B</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:22"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">C</font> = <font color="Maroon">B</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> as    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<a NAME="E3:22"/>
<font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/>
<a NAME="E4:22"/><b>then </b>
<font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:22"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="measure1.html#T1" target="_self">Th1</a>, <a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>;<br/>
<a NAME="E6:22"/>
<font color="Maroon">M</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E7:22"/><b>then </b>
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font> &amp;  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">C</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:22"/>
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="supinf_2.html#T20">SUPINF_2:20</a></i>;<br/>


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