<?xml version="1.0"?>
<div class="add">

<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="measure1.html#M2" target="_self">measure_zero</a> of <font color="Maroon">M</font>, <font color="Maroon">B</font> be    <a href="measure1.html#M2" target="_self">measure_zero</a> of <font color="Maroon">M</font>;<br/>







<a NAME="E1:32"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">M</font> <a href="measure1.html#K1" target="_self">.</a> <font color="Maroon">A</font> <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> <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="E2:32"/>
<font color="Maroon">M</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:32"/><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="E4:32"/>
<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> <a href="supinf_2.html#K1">0.</a>  <a href="supinf_2.html#K2">+</a> <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:32"/><b>then </b>
<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>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i><a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/>
<a NAME="E6:32"/><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="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="E7:32"/>
<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">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
<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="E9:32"/><b>then </b><i><font color="Green">E26</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="E10:32"/>
<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="E11:32"/><b>then </b>
<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>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E12:32"/><b>then </b>
<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>  <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/>
<b>hence </b><a NAME="E13:32"/>
( <font color="Maroon">A</font> <a href="measure1.html#K2" target="_self">\/</a> <font color="Maroon">B</font> is    <a href="measure1.html#M2" target="_self">measure_zero</a> of <font color="Maroon">M</font> &amp; <font color="Maroon">A</font> <a href="measure1.html#K3" target="_self">/\</a> <font color="Maroon">B</font> is    <a href="measure1.html#M2" target="_self">measure_zero</a> of <font color="Maroon">M</font> &amp; <font color="Maroon">A</font> <a href="measure1.html#K4" target="_self">\</a> <font color="Maroon">B</font> is    <a href="measure1.html#M2" target="_self">measure_zero</a> of <font color="Maroon">M</font> )
 <b>by </b><i>, <a class="txt" href="measure1.html#E1:32"><i><font color="Green">E21</font></i></a>, </i>;<br/>


</div>
