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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">sigma_Measure</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">B1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B2</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:29"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">B1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">B2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> )
 ;<br/>

<b>let </b><font color="Maroon">C1</font> be    <a href="measure3.html#M1" target="_self">thin</a> of <font color="Maroon">M</font>, <font color="Maroon">C2</font> be    <a href="measure3.html#M1" target="_self">thin</a> of <font color="Maroon">M</font>;<br/>

<b>assume </b><a NAME="E2:29"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C2</font>
 ;<br/>

<b>consider </b><font color="Maroon">D1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:29"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">D1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D1</font> &amp; <font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">D1</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">D2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:29"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">D2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">C2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font> &amp; <font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">D2</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  )
 <b>by </b><i/>;<br/>
<a NAME="E7:29"/>
( <font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D2</font> )
 
<b>by </b><i><a class="ref" href="measure3.html#T3" target="_self">Th3</a>, , <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E8:29"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:29"/>
( <font color="Maroon">B2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D1</font> )
 
<b>by </b><i><a class="ref" href="measure3.html#T3" target="_self">Th3</a>, , <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E10:29"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">B2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B1</font> = <font color="Maroon">B1</font>, <font color="Maroon">B2</font> = <font color="Maroon">B2</font>, <font color="Maroon">D1</font> = <font color="Maroon">D1</font>, <font color="Maroon">D2</font> = <font color="Maroon">D2</font> as    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="measure3.html#T2" target="_self">Th2</a>, , </i>;<br/>
<a NAME="E12:29"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="measure1.html#K2">\/</a> <font color="Maroon">D2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="measure1.html#T62">MEASURE1:62</a></i>;<br/>
<a NAME="E13:29"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="measure1.html#K2">\/</a> <font color="Maroon">D2</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">.</a> <font color="Maroon">B2</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">.</a> <font color="Maroon">D2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="measure1.html#T64">MEASURE1:64</a></i>;<br/>
<a NAME="E14:29"/>
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B2</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">.</a> <font color="Maroon">D2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B2</font>
 
<b>by </b><i>, <a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/>
<a NAME="E15:29"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B2</font>
 
<b>by </b><i><a class="txt" href="measure3.html#E4:29"><i><font color="Green">E27</font></i></a>, , <a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/>
<a NAME="E16:29"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="measure1.html#K2">\/</a> <font color="Maroon">D1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="measure3.html#E2:29"><i><font color="Green">E26</font></i></a>, <a class="ref" href="measure1.html#T62">MEASURE1:62</a></i>;<br/>
<a NAME="E17:29"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="measure1.html#K2">\/</a> <font color="Maroon">D1</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">.</a> <font color="Maroon">B1</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">.</a> <font color="Maroon">D1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="measure1.html#T64">MEASURE1:64</a></i>;<br/>
<a NAME="E18:29"/>
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B1</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">.</a> <font color="Maroon">D1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B1</font>
 
<b>by </b><i>, <a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/>
<a NAME="E19:29"/><b>then </b>
<font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">M</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B1</font>
 
<b>by </b><i><a class="txt" href="measure3.html#E8:29"><i><font color="Green">E30</font></i></a>, <a class="txt" href="measure3.html#E10:29"><i><font color="Green">E31</font></i></a>, <a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/>
<b>hence </b><a NAME="E20:29"/>
<font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">B2</font>
 <b>by </b><i><a class="txt" href="measure3.html#E6:29"><i><font color="Green">E29</font></i></a>, <a class="ref" href="supinf_1.html#T22">SUPINF_1:22</a></i>;<br/>


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