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

<b>let </b><font color="Maroon" title="c1">e</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:60"/><i><font color="Green" title="E39">A1</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">e</font>
 <b>and </b><br/><a NAME="E2:60"/><i><font color="Green" title="E40">A2</font></i>: 
<font color="Maroon" title="c1">e</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1
 ;<br/>

<b>set </b><font color="Maroon" title="c2">f</font> =  <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a> ;<br/>
<b>set </b><font color="Maroon" title="c3">g</font> =  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font>;<br/>
<b>set </b><font color="Maroon" title="c4">h</font> = <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span>;<br/>
<a NAME="E3:60"/><i><font color="Green" title="E41">A3</font></i>: 
( <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:60"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="asympt_1.html#E23"><i><font color="Green" title="E20">Lm16</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">d</font> =  <a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p1">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span>;<br/>
<a NAME="E4:60"/>
0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">e</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 
<b>by </b><i><a class="txt" href="asympt_1.html#E1:60"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:60"/><b>then </b>
 <a href="power.html#K6" title="POWER:func.6">log</a> 2,1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p1">(<span class="default"><font color="Maroon" title="c1">e</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="power.html#T65" title="POWER:th.65">POWER:65</a></i>;<br/>
<a NAME="E6:60"/><b>then </b><i><font color="Green" title="E42">A4</font></i>: 
 <a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p1">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="power.html#T59" title="POWER:th.59">POWER:59</a></i>;<br/>
<a NAME="E7:60"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">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> <b> such that </b><br/><a NAME="E9:60"/><i><font color="Green" title="E43">A5</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c6">N</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"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 0</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:60"><i><font color="Green" title="E41">A3</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="E10:60"/>
 ex <font color="Olive" title="b1">N</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <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">N</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</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">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Olive" title="b2">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Olive" title="b2">n</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c7">N1</font> =  <a href="asympt_0.html#K4" title="ASYMPT_0:func.4">max</a> 2,<font color="Maroon" title="c6">N</font>;<br/>
<a NAME="E1:60_1"/><i><font color="Green" title="E44">A6</font></i>: 
(  <a href="asympt_0.html#K4" title="ASYMPT_0:func.4">max</a> 2,<font color="Maroon" title="c6">N</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp;  <a href="asympt_0.html#K4" title="ASYMPT_0:func.4">max</a> 2,<font color="Maroon" title="c6">N</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c6">N</font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c8">N1</font> =  <a href="asympt_0.html#K4" title="ASYMPT_0:func.4">max</a> 2,<font color="Maroon" title="c6">N</font>;<br/><b>let </b><font color="Maroon" title="c9">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:60_1_1"/><i><font color="Green" title="E45">A7</font></i>: 
<font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c8">N1</font>
 ;<br/><a NAME="E2:60_1_1"/><b>then </b><i><font color="Green" title="E46">A8</font></i>: 
( <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c6">N</font> )
 <b>by </b><i><a class="txt" href="asympt_1.html#E1:60_1"><i><font color="Green" title="E44">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E3:60_1_1"/><b>then </b><i><font color="Green" title="E47">A9</font></i>: 
 <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"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p4">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 0</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16
 <b>by </b><i><a class="txt" href="asympt_1.html#E9:60"><i><font color="Green" title="E43">A5</font></i></a></i>;<br/><a NAME="E4:60_1_1"/>
 <a href="power.html#K6" title="POWER:func.6">log</a> 2,2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E2:60_1_1"><i><font color="Green" title="E46">A8</font></i></a>, <a class="ref" href="pre_ff.html#T12" title="PRE_FF:th.12">PRE_FF:12</a></i>;<br/><a NAME="E5:60_1_1"/><b>then </b><i><font color="Green" title="E48">A10</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font>
 <b>by </b><i><a class="ref" href="power.html#T60" title="POWER:th.60">POWER:60</a></i>;<br/><i><font color="Green" title="E49">A11</font></i>: <span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font> = 
<span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</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> <font color="Maroon" title="c1">e</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">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/>.= 
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</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> <font color="Maroon" title="c1">e</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font></span>)</span>
<b>by </b><i><a class="txt" href="asympt_1.html#E1:60_1"><i><font color="Green" title="E44">A6</font></i></a>, <a class="txt" href="asympt_1.html#E1:60_1_1"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="asympt_1.html#D2" target="_self" title="ASYMPT_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span>
<b>by </b><i><a class="txt" href="asympt_1.html#E1:60_1"><i><font color="Green" title="E44">A6</font></i></a>, <a class="txt" href="asympt_1.html#E1:60_1_1"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="asympt_1.html#D3" target="_self" title="ASYMPT_1:def.3">Def3</a></i>
;<br/><a NAME="E7:60_1_1"/><i><font color="Green" title="E50">A12</font></i>: 
<font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="asympt_1.html#E1:60_1"><i><font color="Green" title="E44">A6</font></i></a>, <a class="txt" href="asympt_1.html#E1:60_1_1"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><a NAME="E8:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/><a NAME="E9:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span> <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> 0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E5:60_1_1"><i><font color="Green" title="E48">A10</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E10:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="asympt_1.html#E6:60_1_1"><i><font color="Green" title="E49">A11</font></i></a>, <a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></i>;<br/><a NAME="E11:60_1_1"/><b>then </b><i><font color="Green" title="E51">A13</font></i>: 
<span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16
 <b>by </b><i><a class="txt" href="asympt_1.html#E3:60_1_1"><i><font color="Green" title="E47">A9</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>;<br/><a NAME="E12:60_1_1"/>
<font color="Maroon" title="c9">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#E2:60_1_1"><i><font color="Green" title="E46">A8</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E13:60_1_1"/><b>then </b>
<font color="Maroon" title="c9">n</font> <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E2:60"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="power.html#T44" title="POWER:th.44">POWER:44</a></i>;<br/><a NAME="E14:60_1_1"/><b>then </b>
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E7:60_1_1"><i><font color="Green" title="E50">A12</font></i></a>, <a class="ref" href="real_2.html#T151" title="REAL_2:th.151">REAL_2:151</a></i>;<br/><a NAME="E15:60_1_1"/><b>then </b>
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30" title="POWER:th.30">POWER:30</a></i>;<br/><a NAME="E16:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E5:60_1_1"><i><font color="Green" title="E48">A10</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E17:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T100" title="XCMPLX_1:th.100">XCMPLX_1:100</a></i>;<br/><a NAME="E18:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">n</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E6:60_1_1"><i><font color="Green" title="E49">A11</font></i></a>, <a class="ref" href="xcmplx_1.html#T100" title="XCMPLX_1:th.100">XCMPLX_1:100</a></i>;<br/><a NAME="E19:60_1_1"/><b>then </b><i><font color="Green" title="E52">A14</font></i>: 
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16
 <b>by </b><i><a class="txt" href="asympt_1.html#E11:60_1_1"><i><font color="Green" title="E51">A13</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E20:60_1_1"/>
<font color="Maroon" title="c9">n</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="asympt_1.html#E1:60_1"><i><font color="Green" title="E44">A6</font></i></a>, <a class="txt" href="asympt_1.html#E1:60_1_1"><i><font color="Green" title="E45">A7</font></i></a>, <a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/><a NAME="E21:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <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> 0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E5:60_1_1"><i><font color="Green" title="E48">A10</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E22:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></i>;<br/><a NAME="E23:60_1_1"/><b>then </b>
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</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,<font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</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,<span class="p3">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16</span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E19:60_1_1"><i><font color="Green" title="E52">A14</font></i></a>, <a class="ref" href="real_2.html#T151" title="REAL_2:th.151">REAL_2:151</a></i>;<br/><a NAME="E24:60_1_1"/><b>then </b>
<font color="Maroon" title="c9">n</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</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,<span class="p3">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 16</span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T57" title="XCMPLX_1:th.57">XCMPLX_1:57</a></i>;<br/><a NAME="E25:60_1_1"/><b>then </b>
<font color="Maroon" title="c9">n</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 16 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T57" title="XCMPLX_1:th.57">XCMPLX_1:57</a></i>;<br/><a NAME="E26:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default">16 <a href="real_1.html#K6" title="REAL_1:func.6">/</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">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E6:60"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E27:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 16
 <b>by </b><i><a class="txt" href="asympt_1.html#E6:60"><i><font color="Green" title="E42">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="E28:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p3">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 16 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E5:60_1_1"><i><font color="Green" title="E48">A10</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/><a NAME="E29:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 16 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span>
 ;<br/><a NAME="E30:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default">8 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 8</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="asympt_1.html#E5:60_1_1"><i><font color="Green" title="E48">A10</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E31:60_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p3">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E32:60_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</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">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c9">n</font></span>)</span>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:60_1"/>
 ex <font color="Olive" title="b1">N</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <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">N</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</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">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Olive" title="b2">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Olive" title="b2">n</font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:60"/>
 ex <font color="Olive" title="b1">N</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <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">N</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</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">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c1">e</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Olive" title="b2">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 8 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Olive" title="b2">n</font></span>)</span>
 ;<br/>


</div>
