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

<b>assume </b><a NAME="E1:52"/><i><font color="Green" title="E34">A1</font></i>: 
 <a href="power.html#K6" title="POWER:func.6">log</a> 2,3 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Omega</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K12" title="ASYMPT_0:func.12">Big_Theta</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c1">f</font> =  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c2">g</font> =  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c3">h</font> = <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">c</font> = <span class="p1">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span>;<br/>
<a NAME="E2:52"/><i><font color="Green" title="E35">A2</font></i>: 
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span>
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:52"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<a NAME="E3:52"/><b>then </b><i><font color="Green" title="E36">A3</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <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">2 <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/>
<a NAME="E4:52"/><i><font color="Green" title="E37">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 <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="asympt_1.html#E1:52"><i><font color="Green" title="E34">A1</font></i></a></i>;<br/>
<div><i><font color="Green" title="E38">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">p</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">p</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>  implies  ex <font color="Olive" title="b1">N1</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 <br/>for <font color="Olive" title="b2">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="b2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">N1</font> holds <br/> <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font> )</span><br/><b>assume </b><a NAME="E1:52_1"/><i><font color="Green" title="E39">A6</font></i>: 
<font color="Maroon" title="c5">p</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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">N1</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 <br/>for <font color="Olive" title="b2">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="b2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">N1</font> holds <br/> <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font></span><br/><b>reconsider </b><font color="Maroon" title="c6">p1</font> = <font color="Maroon" title="c5">p</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/><b>set </b><font color="Maroon" title="c7">N1</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>,2;<br/><a NAME="E3:52_1"/><i><font color="Green" title="E40">A7</font></i>: 
(  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>,2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span> &amp;  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>,2 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 )
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/><a NAME="E4:52_1"/><b>then </b><i><font color="Green" title="E41">A8</font></i>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>,2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:52_1"/>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>,2 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T16" title="XXREAL_0:th.16">XXREAL_0:16</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c8">N1</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>,2 as    <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>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><b>take </b><font color="Maroon" title="c9">N1</font> = <font color="Maroon" title="c8">N1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c9">N1</font> holds <br/> <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font></span><br/><b>let </b><font color="Maroon" title="c10">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c9">N1</font> implies  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font> )</span><br/><b>assume </b><a NAME="E7:52_1"/><i><font color="Green" title="E42">A9</font></i>: 
<font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c9">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font></span><br/><a NAME="E8:52_1"/>
<font color="Maroon" title="c5">p</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="asympt_1.html#E1:52_1"><i><font color="Green" title="E39">A6</font></i></a>, <a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/><a NAME="E9:52_1"/><b>then </b><i><font color="Green" title="E43">A10</font></i>: 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</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> 
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>;<br/><a NAME="E10:52_1"/>
<span class="p1"><a href="int_1.html#K2" title="INT_1:func.2">[/</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="int_1.html#D5" title="INT_1:def.5">INT_1:def 5</a></i>;<br/><a NAME="E11:52_1"/><b>then </b><i><font color="Green" title="E44">A11</font></i>: 
<font color="Maroon" title="c9">N1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E12:52_1"/><i><font color="Green" title="E45">A12</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="asympt_1.html#E9:52_1"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><a NAME="E13:52_1"/><i><font color="Green" title="E46">A13</font></i>: 
<font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="asympt_1.html#E4:52_1"><i><font color="Green" title="E41">A8</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E14:52_1"/><i><font color="Green" title="E47">A14</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E10"><i><font color="Green" title="E7">Lm4</font></i></a></i>;<br/><a NAME="E15:52_1"/>
<span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="asympt_1.html#D3" target="_self" title="ASYMPT_1:def.3">Def3</a></i>;<br/><b>then </b><i><font color="Green" title="E48">A15</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="txt" href="asympt_1.html#E14:52_1"><i><font color="Green" title="E47">A14</font></i></a>, <a class="ref" href="asympt_1.html#D3" target="_self" title="ASYMPT_1:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></i>
<br/>.= 
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span></span>)</span>

;<br/><a NAME="E17:52_1"/>
<font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="txt" href="asympt_1.html#E11:52_1"><i><font color="Green" title="E44">A11</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E18:52_1"/><b>then </b>
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="asympt_1.html#E12:52_1"><i><font color="Green" title="E45">A12</font></i></a>, <a class="txt" href="asympt_1.html#E13"><i><font color="Green" title="E10">Lm6</font></i></a></i>;<br/><a NAME="E19:52_1"/><b>then </b>
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></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"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E9:52_1"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="power.html#T38" title="POWER:th.38">POWER:38</a></i>;<br/><a NAME="E20:52_1"/><b>then </b>
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> 1
 <b>by </b><i><a class="txt" href="asympt_1.html#E4:52"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E21:52_1"/><b>then </b>
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c6">p1</font>
 <b>by </b><i><a class="ref" href="power.html#T30" title="POWER:th.30">POWER:30</a></i>;<br/><a NAME="E22:52_1"/><b>then </b>
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c5">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E9:52_1"><i><font color="Green" title="E43">A10</font></i></a>, <a class="ref" href="real_2.html#T152" title="REAL_2:th.152">REAL_2:152</a></i>;<br/><a NAME="E23:52_1"/><b>then </b>
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>;<br/><a NAME="E24:52_1"/><b>then </b>
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T218" title="XCMPLX_1:th.218">XCMPLX_1:218</a></i>;<br/><a NAME="E25:52_1"/><b>then </b><i><font color="Green" title="E49">A16</font></i>: 
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="power.html#T33" title="POWER:th.33">POWER:33</a></i>;<br/><a NAME="E26:52_1"/><i><font color="Green" title="E50">A17</font></i>: 
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><a NAME="E27:52_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1
 <b>by </b><i><a class="txt" href="asympt_1.html#E2:52"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E28:52_1"/><b>then </b>
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E13:52_1"><i><font color="Green" title="E46">A13</font></i></a>, <a class="ref" href="power.html#T44" title="POWER:th.44">POWER:44</a></i>;<br/><a NAME="E29:52_1"/><b>then </b>
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E26:52_1"><i><font color="Green" title="E50">A17</font></i></a>, <a class="ref" href="real_2.html#T151" title="REAL_2:th.151">REAL_2:151</a></i>;<br/><a NAME="E30:52_1"/><b>then </b>
<font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="ref" href="power.html#T33" title="POWER:th.33">POWER:33</a></i>;<br/><a NAME="E31:52_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c10">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="txt" href="asympt_1.html#E16:52_1"><i><font color="Green" title="E48">A15</font></i></a>, <a class="ref" href="power.html#T33" title="POWER:th.33">POWER:33</a></i>;<br/><a NAME="E32:52_1"/><b>then </b><i><font color="Green" title="E51">A18</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E25:52_1"><i><font color="Green" title="E49">A16</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E33:52_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</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> 
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:52_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="txt" href="asympt_1.html#E7:52_1"><i><font color="Green" title="E42">A9</font></i></a>, <a class="txt" href="asympt_1.html#E16:52_1"><i><font color="Green" title="E48">A15</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><b>hence </b><a NAME="E34:52_1"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p5">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c10">n</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">p</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E32:52_1"><i><font color="Green" title="E51">A18</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E6:52"/><b>then </b><i><font color="Green" title="E39">A19</font></i>: 
<span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="ref" href="seq_2.html#D6" title="SEQ_2:def.6">SEQ_2:def 6</a></i>;<br/>
<a NAME="E7:52"/><b>then </b><i><font color="Green" title="E40">A20</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p3">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></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="txt" href="asympt_1.html#E5:52"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="seq_2.html#D7" title="SEQ_2:def.7">SEQ_2:def 7</a></i>;<br/>
<a NAME="E8:52"/><b>then </b><i><font color="Green" title="E41">A21</font></i>: 
(  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="asympt_1.html#E6:52"><i><font color="Green" title="E39">A19</font></i></a>, <a class="ref" href="asympt_0.html#T16" title="ASYMPT_0:th.16">ASYMPT_0:16</a></i>;<br/>
<a NAME="E9:52"/><b>then </b><i><font color="Green" title="E42">A22</font></i>: 
(  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Omega</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="asympt_0.html#T19" title="ASYMPT_0:th.19">ASYMPT_0:19</a></i>;<br/>
<b>thus </b><a NAME="E10:52"/>
 <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E6:52"><i><font color="Green" title="E39">A19</font></i></a>, <a class="txt" href="asympt_1.html#E7:52"><i><font color="Green" title="E40">A20</font></i></a>, <a class="ref" href="asympt_0.html#T16" title="ASYMPT_0:th.16">ASYMPT_0:16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Omega</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> &amp; not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K12" title="ASYMPT_0:func.12">Big_Theta</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span> )</span><br/>

<b>thus </b><a NAME="E11:52"/>
not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K11" title="ASYMPT_0:func.11">Big_Omega</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E8:52"><i><font color="Green" title="E41">A21</font></i></a>, <a class="ref" href="asympt_0.html#T19" title="ASYMPT_0:th.19">ASYMPT_0:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K12" title="ASYMPT_0:func.12">Big_Theta</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span></span><br/>

<b>thus </b><a NAME="E12:52"/>
not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,3</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K12" title="ASYMPT_0:func.12">Big_Theta</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E9:52"><i><font color="Green" title="E42">A22</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
