<?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">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be    <a href="measure4.html#M1" target="_self">C_Measure</a> of <font color="Maroon">X</font>;<br/>







<b>assume </b><a NAME="E1:15"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font>, <font color="Maroon">B</font> = <font color="Maroon">B</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> ;<br/>
<b>set </b><font color="Maroon">D</font> = <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font>;<br/>
<a NAME="E3:15"/>
for <font color="Olive">W</font>, <font color="Olive">Z</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> &amp; <font color="Olive">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Olive">W</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Olive">Z</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">W</font> <a href="subset_1.html#K4">\/</a> <font color="Olive">Z</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">W</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">Z</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> &amp; <font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> )
 ;<br/>

<b>set </b><font color="Maroon">W1</font> = <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font>;<br/>
<a NAME="E2:15_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T33">XBOOLE_1:33</a></i>;<br/>
<b>set </b><font color="Maroon">W2</font> = <font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font>;<br/>
<a NAME="E3:15_1"/>
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</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="E4:15_1"/><b>then </b>
<font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E5:15_1"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E6:15_1"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<b>set </b><font color="Maroon">Z1</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font>;<br/>
<a NAME="E7:15_1"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E8:15_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T51">XBOOLE_1:51</a></i>;<br/>
<i><font color="Green">E35</font></i>: <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span> = 
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T51">XBOOLE_1:51</a></i>
<br/>.= 
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span></span>)</span>
<b>by </b><i>, , , </i>
;<br/>
<a NAME="E10:15_1"/>
<font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T33">XBOOLE_1:33</a></i>;<br/>
<a NAME="E11:15_1"/><b>then </b>
( <font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> &amp; <font color="Maroon">B</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a>, <a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/>
<a NAME="E12:15_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E13:15_1"/>
( <font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">B</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">B</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a>, <a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>;<br/>
<a NAME="E14:15_1"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E15:15_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i>, <a class="txt" href="measure4.html#E1:15_1"><i><font color="Green">E24</font></i></a>, </i>;<br/>
<a NAME="E16:15_1"/>
<font color="Maroon">C</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E17:15_1"/><b>then </b><i><font color="Green">E39</font></i>: 
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span> &amp;  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="measure1.html#D4">MEASURE1:def 4</a></i>;<br/>
<a NAME="E18:15_1"/><b>then </b>
<a href="supinf_2.html#K1">0.</a>  <a href="supinf_2.html#K2">+</a> <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="measure1.html#T4">MEASURE1:4</a></i>;<br/>
<a NAME="E19:15_1"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/>
<a NAME="E20:15_1"/>
<font color="Maroon">C</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E21:15_1"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="measure1.html#D4">MEASURE1:def 4</a></i>;<br/>
<a NAME="E22:15_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i><a class="txt" href="measure4.html#E1:15"><i><font color="Green">E23</font></i></a>, <a class="txt" href="measure4.html#E2:15_1"><i><font color="Green">E25</font></i></a>, , <a class="ref" href="measure1.html#T4">MEASURE1:4</a></i>;<br/>
<a NAME="E23:15_1"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E24:15_1"/>
<font color="Maroon">C</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E25:15_1"/><b>then </b><i><font color="Green">E56</font></i>: 
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font> &amp;  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="measure1.html#D4">MEASURE1:def 4</a></i>;<br/>
<a NAME="E26:15_1"/>
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="measure4.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E27:15_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="measure1.html#T4">MEASURE1:4</a></i>;<br/>
<a NAME="E28:15_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/>
<a NAME="E29:15_1"/>
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E30:15_1"/>
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">Z</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="measure4.html#E5:15_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="supinf_1.html#T22">SUPINF_1:22</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:15"/>
<font color="Maroon">A</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font>
 <b>by </b><i/>;<br/>


</div>
