<?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="prob_1.html#M1">SetSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:29"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="prob_1.html#V3">non-decreasing</a>
 ;<br/>

<a NAME="E2:29"/>
 <a href="prob_3.html#K6">@Partial_Diff_Union</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a>  <a href="prob_3.html#K3">Partial_Diff_Union</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="prob_3.html#D7">PROB_3:def 7</a></i>;<br/>
<b>hence </b><a NAME="E3:29"/>
( <span class="p1">(<span class="default"><a href="prob_3.html#K6">@Partial_Diff_Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prob_4.html#K1" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="prob_4.html#K1" target="_self">.</a> 0 &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><a href="prob_3.html#K6">@Partial_Diff_Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prob_4.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_4.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="measure1.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_4.html#K1" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="prob_4.html#E1:29"><i><font color="Green">E22</font></i></a>, <a class="ref" href="prob_4.html#T17" target="_self">Th17</a></i>;<br/>


</div>
