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

<b>let </b><font color="Maroon">D1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font>, <a href="numbers.html#K6">ExtREAL</a> , <font color="Maroon">D2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font>, <a href="numbers.html#K6">ExtREAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> holds <br/><font color="Maroon">D1</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Olive">A</font>
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> holds <br/><font color="Maroon">D2</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Olive">A</font>
 ;<br/>

<a NAME="E3:22_1_2"/><i><font color="Green">E33</font></i>: 
(  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">D1</font> &amp;  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">D2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:22_1_2"/>
for <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font> holds <br/><font color="Maroon">D1</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D2</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:22_1_2_1"/><i><font color="Green">E34</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>
 ;<br/>

<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> ;<br/>
<font color="Maroon">D1</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">A</font> = 
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">A</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">D2</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">A</font>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E4:22_1_2_1"/>
<font color="Maroon">D1</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D2</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">A</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:22_1_2"/>
<font color="Maroon">D1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D2</font>
 <b>by </b><i><a class="ref" href="measure4.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
