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<b>let </b><font color="Maroon" title="c1">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">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>assume </b><a NAME="E1:63"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">q</font> = <font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font> as  <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>  <b>by </b><i><a class="txt" href="entropy1.html#E1:63"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="entropy1.html#T10" target="_self" title="ENTROPY1:th.10">Th10</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">qq</font> =  <a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font>;<br/>
<a NAME="E3:63"/><i><font color="Green" title="E56">A2</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">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="c2">p</font>
 
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>;<br/>
<a NAME="E4:63"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">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="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="entropy1.html#T47" target="_self" title="ENTROPY1:th.47">Th47</a></i>;<br/>
<a NAME="E5:63"/><b>then </b><i><font color="Green" title="E57">A3</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">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="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</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="E6:63"/><i><font color="Green" title="E58">A4</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <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">p</font>
 
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>;<br/>
<a NAME="E7:63"/><i><font color="Green" title="E59">A5</font></i>: 
 <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="c2">p</font></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="c2">p</font>
 
<b>by </b><i><a class="ref" href="entropy1.html#D6" target="_self" title="ENTROPY1:def.6">Def6</a></i>;<br/>
<a NAME="E8:63"/><b>then </b><i><font color="Green" title="E60">A6</font></i>: 
 <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="c2">p</font></span>)</span> <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">p</font>
 
<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="E9:63"/>
 <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="c2">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="c2">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="c2">p</font>
 
<b>by </b><i><a class="txt" href="entropy1.html#E7:63"><i><font color="Green" title="E59">A5</font></i></a>, <a class="ref" href="matrprob.html#T30" title="MATRPROB:th.30">MATRPROB:30</a></i>;<br/>
<a NAME="E10:63"/><b>then </b><i><font color="Green" title="E61">A7</font></i>: 
 <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="c2">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="c2">p</font></span>)</span></span>)</span> <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">p</font>
 
<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="E11:63"/><b>then </b>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span> <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">p</font>
 
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>;<br/>
<a NAME="E12:63"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="entropy1.html#E6:63"><i><font color="Green" title="E58">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="E13:63"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="integra5.html#T2" title="INTEGRA5:th.2">INTEGRA5:2</a></i>;<br/>
<a NAME="E14:63"/><b>then </b><i><font color="Green" title="E62">A8</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:63_1"/><i><font color="Green" title="E63">A9</font></i>: 
<font color="Maroon" title="c5">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#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font></span>)</span>
 ;<br/><a NAME="E2:63_1"/>
( <font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">q</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span> )
 <b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="ref" href="entropy1.html#D1" target="_self" title="ENTROPY1:def.1">Def1</a>, <a class="ref" href="rvsum_1.html#T66" title="RVSUM_1:th.66">RVSUM_1:66</a></i>;<br/><a NAME="E3:63_1"/><b>then </b><i><font color="Green" title="E64">A10</font></i>: 
<span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E1:63"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="ref" href="entropy1.html#T50" target="_self" title="ENTROPY1:th.50">Th50</a></i>;<br/><a NAME="E4:63_1"/><i><font color="Green" title="E65">A11</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="rvsum_1.html#T66" title="RVSUM_1:th.66">RVSUM_1:66</a></i>;<br/><i><font color="Green" title="E66">A12</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> = 
<font color="Maroon" title="c1">r</font> <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="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T66" title="RVSUM_1:th.66">RVSUM_1:66</a></i>
<br/>.= 
<font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E10:63"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="ref" href="rvsum_1.html#T86" title="RVSUM_1:th.86">RVSUM_1:86</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span></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="c2">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span>

;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_1_2"/>
( <font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">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>  or <font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</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="63_1_2_1"><b>suppose </b></a><a NAME="E1:63_1_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">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="E2:63_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E8:63"><i><font color="Green" title="E60">A6</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="txt" href="entropy1.html#E3:63_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="txt" href="entropy1.html#E4:63_1"><i><font color="Green" title="E65">A11</font></i></a>, <a class="txt" href="entropy1.html#E5:63_1"><i><font color="Green" title="E66">A12</font></i></a>, <a class="ref" href="entropy1.html#D6" target="_self" title="ENTROPY1:def.6">Def6</a></i>;<br/><b>hence </b><a NAME="E3:63_1_2_1"/>
<span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font>
 <b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E6:63"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="entropy1.html#E14:63"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_2_2"><b>suppose </b></a><a NAME="E1:63_1_2_2"/>
<font color="Maroon" title="c2">p</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">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="E2:63_1_2_2"/>
<span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p4">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">k</font>
 <b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E6:63"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="entropy1.html#E14:63"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="entropy1.html#E1:63_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="txt" href="entropy1.html#E3:63_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="txt" href="entropy1.html#E4:63_1"><i><font color="Green" title="E65">A11</font></i></a>, <a class="txt" href="entropy1.html#E5:63_1"><i><font color="Green" title="E66">A12</font></i></a>, <a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E16:63"/>
 <a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r</font></span>)</span></span>)</span> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">r</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K14" title="RVSUM_1:func.14">mlt</a> <font color="Maroon" title="c2">p</font>,<span class="p3">(<span class="default"><a href="entropy1.html#K3" title="ENTROPY1:func.3">FinSeq_log</a> 2,<font color="Maroon" title="c2">p</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="entropy1.html#E3:63"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="entropy1.html#E5:63"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="entropy1.html#E6:63"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="entropy1.html#E14:63"><i><font color="Green" title="E62">A8</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


</div>
