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

<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>for <font color="Olive" title="b1">f</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">p</font> being  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> &amp;  <a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Olive" title="b2">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Olive" title="b1">f</font></span>)</span>;<br/>
<a NAME="E1:63"/><i><font color="Green" title="E62">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">f</font> be    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>;<br/>



<b>assume </b><a NAME="E1:63_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> &amp;  <a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:63_1"/><b>then </b><i><font color="Green" title="E63">A2</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E3:63_1"/><b>then </b><i><font color="Green" title="E64">A3</font></i>: 
 <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="nat_4.html#T50" target="_self" title="NAT_4:th.50">Th50</a>, <a class="ref" href="rvsum_1.html#T102" title="RVSUM_1:th.102">RVSUM_1:102</a></i>;<br/>
<a NAME="E4:63_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:63_1"/>
<font color="Maroon" title="c2">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="nat_4.html#E2:63_1"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="nat_4.html#E3:63_1"><i><font color="Green" title="E64">A3</font></i></a>, <a class="ref" href="nat_3.html#T21" title="NAT_3:th.21">NAT_3:21</a>, <a class="ref" href="rvsum_1.html#T124" title="RVSUM_1:th.124">RVSUM_1:124</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:63"/><i><font color="Green" title="E63">A4</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>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">n</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="E1:63_2"/><i><font color="Green" title="E64">A5</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">n</font>]
 ;<br/>

<a NAME="E2:63_2"/>
for <font color="Olive" title="b1">f</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">p</font> being  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> &amp;  <a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Olive" title="b2">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Olive" title="b1">f</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">f</font> be    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>;<br/>



<b>assume </b><a NAME="E1:63_2_1"/><i><font color="Green" title="E65">A6</font></i>: 
( <font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">g</font> being    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c5">d</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> <b> such that </b><br/><a NAME="E3:63_2_1"/><i><font color="Green" title="E66">A7</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">d</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T22" title="FINSEQ_2:th.22">FINSEQ_2:22</a></i>;<br/>
<a NAME="E4:63_2_1"/><i><font color="Green" title="E67">A8</font></i>: 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="nat_4.html#E1:63_2_1"><i><font color="Green" title="E65">A6</font></i></a>, <a class="txt" href="nat_4.html#E3:63_2_1"><i><font color="Green" title="E66">A7</font></i></a>, <a class="ref" href="rvsum_1.html#T126" title="RVSUM_1:th.126">RVSUM_1:126</a></i>;<br/>
<a NAME="E5:63_2_1"/><b>then </b><i><font color="Green" title="E68">A9</font></i>: 
 <a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E6:63_2_1"/><i><font color="Green" title="E69">A10</font></i>: 
<font color="Maroon" title="c5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="nat_4.html#E4:63_2_1"><i><font color="Green" title="E67">A8</font></i></a></i>;<br/>
<a NAME="E7:63_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">d</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="nat_4.html#E3:63_2_1"><i><font color="Green" title="E66">A7</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E8:63_2_1"/><b>then </b><i><font color="Green" title="E70">A11</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="txt" href="nat_4.html#E1:63_2_1"><i><font color="Green" title="E65">A6</font></i></a>, <a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
<font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c5">d</font></span>)</span>
<b>by </b><i><a class="txt" href="nat_4.html#E3:63_2_1"><i><font color="Green" title="E66">A7</font></i></a>, <a class="ref" href="rvsum_1.html#T126" title="RVSUM_1:th.126">RVSUM_1:126</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p2">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c5">d</font></span>)</span>
<b>by </b><i><a class="txt" href="nat_4.html#E5:63_2_1"><i><font color="Green" title="E68">A9</font></i></a>, <a class="txt" href="nat_4.html#E6:63_2_1"><i><font color="Green" title="E69">A10</font></i></a>, <a class="ref" href="nat_3.html#T28" title="NAT_3:th.28">NAT_3:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c5">d</font></span>)</span>
<b>by </b><i><a class="txt" href="nat_4.html#E1:63_2"><i><font color="Green" title="E64">A5</font></i></a>, <a class="txt" href="nat_4.html#E5:63_2_1"><i><font color="Green" title="E68">A9</font></i></a>, <a class="txt" href="nat_4.html#E8:63_2_1"><i><font color="Green" title="E70">A11</font></i></a></i>
<br/>.= 
 <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c5">d</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T104" title="RVSUM_1:th.104">RVSUM_1:104</a></i>
<br/>.= 
 <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">d</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="nat_4.html#E6:63_2_1"><i><font color="Green" title="E69">A10</font></i></a>, <a class="ref" href="nat_4.html#T52" target="_self" title="NAT_4:th.52">Th52</a></i>
<br/>.= 
 <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="wsierp_1.html#K2" title="WSIERP_1:func.2">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">d</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="nat_4.html#T51" target="_self" title="NAT_4:th.51">Th51</a></i>
;<br/>
<b>hence </b><a NAME="E10:63_2_1"/>
<font color="Maroon" title="c3">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c2">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="nat_4.html#E3:63_2_1"><i><font color="Green" title="E66">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:63_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:63"/><i><font color="Green" title="E64">A12</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">S<sub>1</sub></font>[<font color="Olive" title="b1">n</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="nat_4.html#E1:63"><i><font color="Green" title="E62">A1</font></i></a>, <a class="txt" href="nat_4.html#E2:63"><i><font color="Green" title="E63">A4</font></i></a>);<br/></i>
<b>let </b><font color="Maroon" title="c1">f</font> be    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>;<br/>



<b>assume </b><a NAME="E4:63"/><i><font color="Green" title="E65">A13</font></i>: 
 <a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E5:63"/>
 ex <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>  st <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 
;<br/>
<b>hence </b><a NAME="E6:63"/>
<font color="Maroon" title="c2">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K5" title="WSIERP_1:func.5">Product</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="nat_4.html#K1" title="NAT_4:func.1">|-count</a> <font color="Maroon" title="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="nat_4.html#E3:63"><i><font color="Green" title="E64">A12</font></i></a>, <a class="txt" href="nat_4.html#E4:63"><i><font color="Green" title="E65">A13</font></i></a></i>;<br/>


</div>
