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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">C</font> be    <a href="measure4.html#M1" target="_self">C_Measure</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </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="E1:27_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> &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> )
 ;<br/><a NAME="E2:27_1"/>
<font color="Maroon">C</font> is <a href="supinf_2.html#V6">nonnegative</a>
 <b>by </b><i/>;<br/><a NAME="E3:27_1"/><b>then </b>
(  <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; <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K1">0.</a>  )
 <b>by </b><i><a class="txt" href="measure4.html#E1:27_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="measure4.html#E4:27_1"><i><font color="Green">E25</font></i></a>, , <a class="ref" href="measure1.html#D4">MEASURE1:def 4</a></i>;<br/><a NAME="E4:27_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 <b>by </b><i><a class="ref" href="supinf_1.html#T22">SUPINF_1:22</a></i>;<br/><a NAME="E5:27_1"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E6:27_1"/><b>then </b>
<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> <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/>;<br/><b>hence </b><a NAME="E7:27_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="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_2.html#T18">SUPINF_2:18</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:27"/>
<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>
 <b>by </b><i/>;<br/>


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