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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="measure1.html#M3">sigma_Measure</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="measure2.html#M1" target="_self">N_Measure_fam</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:18"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is    <a href="measure1.html#M4">measure_zero</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:18"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is    <a href="measure1.html#M4">measure_zero</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:18_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="supinf_2.html#D14">SUPINF_2:def 14</a></i>;<br/>
<a NAME="E3:18_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="prob_1.html#K1">.</a> 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="measure2.html#E2:18_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font> <a href="prob_1.html#K1">.</a> 0
;<br/>

<b>thus </b><a NAME="E4:18_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="prob_1.html#K1">.</a> 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="prob_1.html#K1">.</a> 0 is    <a href="measure1.html#M4">measure_zero</a> of <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="measure2.html#E1:18"><i><font color="Green">E15</font></i></a>, <a class="txt" href="measure2.html#E3:18_1"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:18"/>
 <a href="measure2.html#K1" target="_self">meet</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="measure1.html#M4">measure_zero</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="measure2.html#T17" target="_self">Th17</a></i>;<br/>


</div>
