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

<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c2">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>set </b><font color="Maroon" title="c3">pp</font> =  <a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p1">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span>;<br/>
<a NAME="E1:59"/><i><font color="Green" title="E52">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="entropy1.html#D6" target="_self" title="ENTROPY1:def.6">Def6</a></i>;<br/>
<a NAME="E2:59"/><b>then </b><i><font color="Green" title="E53">A2</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E3:59"/><i><font color="Green" title="E54">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <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">p</font>
 
<b>by </b><i><a class="txt" href="entropy1.html#E1:59"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="matrprob.html#T30" title="MATRPROB:th.30">MATRPROB:30</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:59_1"/><i><font color="Green" title="E55">A4</font></i>: 
<font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c1">p</font>
 ;<br/><b>thus </b><a NAME="E2:59_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">q</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">p</font> &amp; ( for <font color="Olive" title="b1">k</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">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font> holds <br/><font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">k</font></span>)</span></span>)</span> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:59_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">q</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">p</font>
 <b>by </b><i><a class="txt" href="entropy1.html#E1:59"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="entropy1.html#E1:59_1"><i><font color="Green" title="E55">A4</font></i></a>, <a class="ref" href="matrprob.html#T30" title="MATRPROB:th.30">MATRPROB:30</a></i>;<br/>

<b>let </b><font color="Maroon" title="c4">k</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="E2:59_1_1"/><i><font color="Green" title="E56">A5</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font>
 ;<br/>

<a NAME="E3:59_1_1"/><i><font color="Green" title="E57">A6</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font> )
 
<b>by </b><i><a class="txt" href="entropy1.html#E3:59"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="entropy1.html#E1:59_1"><i><font color="Green" title="E55">A4</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E4:59_1_1"/><i><font color="Green" title="E58">A7</font></i>: 
<font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="entropy1.html#E1:59_1"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="entropy1.html#E2:59_1_1"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="rvsum_1.html#T86" title="RVSUM_1:th.86">RVSUM_1:86</a></i>;<br/>
<a NAME="E5:59_1_1"/><i><font color="Green" title="E59">A8</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span>
 
<b>by </b><i><a class="txt" href="entropy1.html#E1:59"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="entropy1.html#E3:59"><i><font color="Green" title="E54">A3</font></i></a>, <a class="txt" href="entropy1.html#E1:59_1"><i><font color="Green" title="E55">A4</font></i></a>, <a class="txt" href="entropy1.html#E2:59_1_1"><i><font color="Green" title="E56">A5</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_1_1_1"/>
( <font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><b>by </b><i><a class="txt" href="entropy1.html#E2:59_1_1"><i><font color="Green" title="E56">A5</font></i></a>, <a class="txt" href="entropy1.html#E3:59_1_1"><i><font color="Green" title="E57">A6</font></i></a>, <a class="ref" href="entropy1.html#D1" target="_self" title="ENTROPY1:def.1">Def1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1_1_1"><b>suppose </b></a><a NAME="E1:59_1_1_1_1"/>
<font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:59_1_1_1_1"/>
<font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E4:59_1_1"><i><font color="Green" title="E58">A7</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_1_1_1_2"><b>suppose </b></a><a NAME="E1:59_1_1_1_2"/>
<font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:59_1_1_1_2"/>
<font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E4:59_1_1"><i><font color="Green" title="E58">A7</font></i></a>, <a class="txt" href="entropy1.html#E5:59_1_1"><i><font color="Green" title="E59">A8</font></i></a>, <a class="ref" href="entropy1.html#D6" target="_self" title="ENTROPY1:def.6">Def6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:59"/><i><font color="Green" title="E55">A9</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">q</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">p</font> &amp; ( for <font color="Olive" title="b1">k</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">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font> holds <br/><font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">k</font></span>)</span></span>)</span> ) )
 ;<br/>

<a NAME="E6:59"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="entropy1.html#E1:59"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="matrprob.html#T30" title="MATRPROB:th.30">MATRPROB:30</a></i>;<br/>
<a NAME="E7:59"/><b>then </b><i><font color="Green" title="E56">A10</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> )
 
<b>by </b><i><a class="txt" href="entropy1.html#E5:59"><i><font color="Green" title="E55">A9</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:59_2"/><i><font color="Green" title="E57">A11</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">q</font>
 ;<br/><a NAME="E2:59_2"/><i><font color="Green" title="E58">A12</font></i>: 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E7:59"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2"><i><font color="Green" title="E57">A11</font></i></a>, <a class="ref" href="rvsum_1.html#T86" title="RVSUM_1:th.86">RVSUM_1:86</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:59_2_1"/>
( <font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><b>by </b><i><a class="txt" href="entropy1.html#E7:59"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2"><i><font color="Green" title="E57">A11</font></i></a>, <a class="ref" href="entropy1.html#D1" target="_self" title="ENTROPY1:def.1">Def1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_1"><b>suppose </b></a><a NAME="E1:59_2_1_1"/><i><font color="Green" title="E59">A13</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="entropy1.html#E5:59"><i><font color="Green" title="E55">A9</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2"><i><font color="Green" title="E57">A11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font>
<b>by </b><i><a class="txt" href="entropy1.html#E2:59_2"><i><font color="Green" title="E58">A12</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2_1_1"><i><font color="Green" title="E59">A13</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="59_2_1_2"><b>suppose </b></a><a NAME="E1:59_2_1_2"/>
<font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:59_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E2:59"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="entropy1.html#E7:59"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2"><i><font color="Green" title="E57">A11</font></i></a>, <a class="ref" href="entropy1.html#D6" target="_self" title="ENTROPY1:def.6">Def6</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c1">p</font>,<span class="p2">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="entropy1.html#E7:59"><i><font color="Green" title="E56">A10</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2"><i><font color="Green" title="E57">A11</font></i></a>, <a class="ref" href="rvsum_1.html#T86" title="RVSUM_1:th.86">RVSUM_1:86</a></i>
<br/>.= 
<font color="Maroon" title="c2">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c4">k</font>
<b>by </b><i><a class="txt" href="entropy1.html#E5:59"><i><font color="Green" title="E55">A9</font></i></a>, <a class="txt" href="entropy1.html#E1:59_2"><i><font color="Green" title="E57">A11</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E9:59"/>
<font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="entropy1.html#E7:59"><i><font color="Green" title="E56">A10</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


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