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

<b>let </b><font color="Maroon">M1</font> be    <a href="measure1.html#M3">sigma_Measure</a> of  <a href="measure3.html#K2" target="_self">COM</a> <font color="Maroon">S</font>,<font color="Maroon">M</font>, <font color="Maroon">M2</font> be    <a href="measure1.html#M3">sigma_Measure</a> of  <a href="measure3.html#K2" target="_self">COM</a> <font color="Maroon">S</font>,<font color="Maroon">M</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:30_1_2"/><i><font color="Green">E128</font></i>: 
for <font color="Olive">B</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/>for <font color="Olive">C</font> being   <a href="measure3.html#M1" target="_self">thin</a> of <font color="Maroon">M</font> holds  <font color="Maroon">M1</font> <a href="supinf_2.html#K13">.</a> <span class="p1">(<span class="default"><font color="Olive">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">C</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">B</font>
 <b>and </b><br/><a NAME="E2:30_1_2"/><i><font color="Green">E129</font></i>: 
for <font color="Olive">B</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/>for <font color="Olive">C</font> being   <a href="measure3.html#M1" target="_self">thin</a> of <font color="Maroon">M</font> holds  <font color="Maroon">M2</font> <a href="supinf_2.html#K13">.</a> <span class="p1">(<span class="default"><font color="Olive">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">C</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">B</font>
 ;<br/>

<a NAME="E3:30_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="measure3.html#K2" target="_self">COM</a> <font color="Maroon">S</font>,<font color="Maroon">M</font> holds <br/><font color="Maroon">M1</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_2_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:30_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="measure3.html#K2" target="_self">COM</a> <font color="Maroon">S</font>,<font color="Maroon">M</font>
 ;<br/>

<b>then consider </b><font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:30_1_2_1"/><i><font color="Green">E130</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp;  ex <font color="Olive">C</font> being   <a href="measure3.html#M1" target="_self">thin</a> of <font color="Maroon">M</font> st <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">C</font> )
 <b>by </b><i/>;<br/>
<font color="Maroon">M1</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">M</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="measure3.html#T2" target="_self">Th2</a>, </i>
<br/>.= 
<font color="Maroon">M2</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="measure3.html#T3" target="_self">Th3</a>, </i>
;<br/>
<b>hence </b><a NAME="E5:30_1_2_1"/>
<font color="Maroon">M1</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font> <a href="supinf_2.html#K13">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:30_1_2"/>
<font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


</div>
