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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#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="measure1.html#M3" target="_self">sigma_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>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="measure1.html#M4" target="_self">measure_zero</a> of <font color="Maroon">M</font>;<br/>









<a NAME="E1:70"/><i><font color="Green">E21</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>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:70"/>
<font color="Maroon">M</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:70"/><b>then </b><i><font color="Green">E24</font></i>: 
(  <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> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font></span>)</span> &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> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font></span>)</span> &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> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:70"/>
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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> <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:70"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font></span>)</span> <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>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/>
<a NAME="E6:70"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E7:70"/><b>then </b><i><font color="Green">E26</font></i>: 
<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> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E8:70"/>
<font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E9:70"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:70"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<a NAME="E11:70"/>
<font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E12:70"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font></span>)</span> <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>
 
<b>by </b><i/>;<br/>
<a NAME="E13:70"/>
<font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font></span>)</span> <a href="measure1.html#K2" target="_self">\/</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T51">XBOOLE_1:51</a></i>;<br/>
<a NAME="E14:70"/><b>then </b>
<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> <a href="supinf_2.html#K1">0.</a>  <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> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="measure1.html#E12:70"><i><font color="Green">E42</font></i></a>, </i>;<br/>
<a NAME="E15:70"/><b>then </b>
<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> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/>
<b>hence </b><a NAME="E16:70"/>
( <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font> &amp; <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  &amp; <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font> )
 <b>by </b><i>, , , <a class="ref" href="measure1.html#T15" target="_self">Th15</a>, , <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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