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

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="measure1.html#M3" title="MEASURE1:mode.3">sigma_Measure</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E20">A1</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E3:29"/><i><font color="Green" title="E21">A2</font></i>: 
( <font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 0 &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="measure1.html#K4" title="MEASURE1:func.4">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="measure2.html#T4" target="_self" title="MEASURE2:th.4">Th4</a></i>;<br/>
<a NAME="E4:29"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c5">G</font> is   <a href="measure1.html#NM4" title="MEASURE1:NM.4">Sep_Sequence</a> of <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="measure2.html#E1:29"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="measure2.html#E3:29"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="measure2.html#T25" target="_self" title="MEASURE2:th.25">Th25</a></i>;<br/>
<a NAME="E5:29"/><i><font color="Green" title="E23">A4</font></i>: 
 <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

<a NAME="E1:29_1"/><i><font color="Green" title="E24">A5</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:29_1"/>
for <font color="Olive" title="b1">m</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/><span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <font color="Olive" title="b1">m</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">m</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:29_1_1"/><i><font color="Green" title="E25">A6</font></i>: 
<font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <b>means </b><span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> $1;<br/>
<a NAME="E2:29_1_1"/><i><font color="Green" title="E26">A7</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> 0 = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> 0
<b>by </b><i><a class="ref" href="supinf_2.html#T63" title="SUPINF_2:th.63">SUPINF_2:63</a></i>
<br/>.= 
<font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E3:29"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> 0
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E3:29_1_1"/><i><font color="Green" title="E27">A8</font></i>: 
for <font color="Olive" title="b1">m</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:29_1_1_2"/><i><font color="Green" title="E28">A9</font></i>: 
<span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c7">m</font>
 ;<br/>

<a NAME="E2:29_1_1_2"/><i><font color="Green" title="E29">A10</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/>
<a NAME="E3:29_1_1_2"/><i><font color="Green" title="E30">A11</font></i>: 
( <font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="measure1.html#K4" title="MEASURE1:func.4">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span> &amp; <font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="measure2.html#E1:29"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="measure2.html#E3:29"><i><font color="Green" title="E21">A2</font></i></a></i>;<br/>
<a NAME="E4:29_1_1_2"/><b>then </b><i><font color="Green" title="E31">A12</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></i>;<br/>
<span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <font color="Maroon" title="c7">m</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E1:29_1_1_2"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="supinf_2.html#T63" title="SUPINF_2:th.63">SUPINF_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E2:29_1_1_2"><i><font color="Green" title="E29">A10</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon" title="c3">M</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">m</font></span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E4:29_1_1_2"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="measure1.html#T61" title="MEASURE1:th.61">MEASURE1:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E2:29_1_1_2"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="measure2.html#E3:29_1_1_2"><i><font color="Green" title="E30">A11</font></i></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>
;<br/>
<b>hence </b><a NAME="E6:29_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:29_1_1"/>
for <font color="Olive" title="b1">m</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="measure2.html#E2:29_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="measure2.html#E3:29_1_1"><i><font color="Green" title="E27">A8</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:29_1_1"/>
<span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <font color="Maroon" title="c6">m</font>
 <b>by </b><i><a class="txt" href="measure2.html#E1:29_1_1"><i><font color="Green" title="E25">A6</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:29_1"/>
 <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K18" title="SUPINF_2:func.18">Ser</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="measure2.html#E1:29_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


</div><b>end;</b></div>
<font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K5" title="MEASURE1:func.5">rng</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K5" title="MEASURE1:func.5">rng</a> <font color="Maroon" title="c5">G</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E1:29"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="measure2.html#E3:29"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="measure2.html#T24" target="_self" title="MEASURE2:th.24">Th24</a></i>
<br/>.= 
 <a href="supinf_2.html#K19" title="SUPINF_2:func.19">SUM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">G</font></span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E4:29"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="measure1.html#D11" title="MEASURE1:def.11">MEASURE1:def 11</a></i>
<br/>.= 
 <a href="supinf_1.html#K6" title="SUPINF_1:func.6">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="measure2.html#E5:29"><i><font color="Green" title="E23">A4</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E7:29"/>
<font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K13" title="SUPINF_2:func.13">.</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><a href="measure1.html#K5" title="MEASURE1:func.5">rng</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_1.html#K6" title="SUPINF_1:func.6">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K17" title="SUPINF_2:func.17">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span>
 ;<br/>


</div>
