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

<span class="kw">set </span><font color="Maroon" title="c1">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/>
<span class="kw">set </span><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/>
<span class="kw">set </span><font color="Maroon" title="c3">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/>
<span class="kw">set </span><font color="Maroon" title="c4">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/>
<span class="kw">assume </span><a NAME="E1:47"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="power.html#K6" title="POWER:func.6">log</a> (2,3) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 159 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 100
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<a NAME="E2:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A2</font></span>: 
<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#NR3" title="XXREAL_0:NR.3">&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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E3:47"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E28">A1</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E31">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:47_1"/><span class="lab"><font color="Green" title="E32">A5</font></span>: 
<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#NR3" title="XXREAL_0:NR.3">&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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="xreal_1.html#T68" title="XREAL_1:th.68">XREAL_1:68</a></span>;<br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font> )</span><br/><span class="kw">assume </span><a NAME="E2:47_1"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font></span><br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/><a NAME="E4:47_1"/><span class="lab"><font color="Green" title="E34">A7</font></span>: 
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></span>;<br/><span class="kw">set </span><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="E5:47_1"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></span>;<br/><a NAME="E6:47_1"/><span class="lab"><font color="Green" title="E36">A9</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T16" title="XXREAL_0:th.16">XXREAL_0:16</a></span>;<br/><a NAME="E7:47_1"/><span class="lab"><font color="Green" title="E37">A10</font></span>: 
 <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
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></span>;<br/><a NAME="E8:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A11</font></span>: 
 <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
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E6:47_1"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="ref" href="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c9">N1</font> = <font color="Maroon" title="c8">N1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font> )</span><br/><a NAME="E10:47_1"/><span class="lab"><font color="Green" title="E39">A12</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="asympt_1.html#E10"><span class="lab"><font color="Green" title="E7">Lm4</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E11:47_1"/><span class="lab"><font color="Green" title="E40">A13</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font></span><br/><a NAME="E12:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="ref" href="asympt_1.html#D3" target="_self" title="ASYMPT_1:def.3">Def3</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A14</font></span>: <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="txt" href="#E10:47_1"><span class="lab"><font color="Green" title="E39">A12</font></span></a>, <a class="ref" href="asympt_1.html#D3" target="_self" title="ASYMPT_1:def.3">Def3</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="power.html#T29" title="POWER:th.29">POWER:29</a></span>
<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="E14:47_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D7" title="INT_1:def.7">INT_1:def 7</a></span>;<br/><a NAME="E15:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E16:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E17:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E4:47_1"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="asympt_1.html#E13"><span class="lab"><font color="Green" title="E10">Lm6</font></span></a></span>;<br/><a NAME="E18:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="power.html#T33" title="POWER:th.33">POWER:33</a></span>;<br/><a NAME="E19:47_1"/><span class="kw">then </span>
<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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>;<br/><a NAME="E20:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T25" title="POWER:th.25">POWER:25</a></span>;<br/><a NAME="E21:47_1"/><span class="kw">then </span>
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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="xreal_1.html#T85" title="XREAL_1:th.85">XREAL_1:85</a></span>;<br/><a NAME="E22:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A15</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="power.html#T28" title="POWER:th.28">POWER:28</a></span>;<br/><a NAME="E23:47_1"/>
<font color="Maroon" title="c10">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47_1"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E24:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A16</font></span>: 
<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#NR3" title="XXREAL_0:NR.3">&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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></span>;<br/><a NAME="E25:47_1"/>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></span>;<br/><a NAME="E26:47_1"/><span class="kw">then </span>
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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:47_1"><span class="lab"><font color="Green" title="E43">A16</font></span></a>, <a class="ref" href="xreal_1.html#T88" title="XREAL_1:th.88">XREAL_1:88</a></span>;<br/><a NAME="E27:47_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="ref" href="power.html#T28" title="POWER:th.28">POWER:28</a></span>;<br/><a NAME="E28:47_1"/><span class="kw">then </span>
<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#NR3" title="XXREAL_0:NR.3">&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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="txt" href="#E13:47_1"><span class="lab"><font color="Green" title="E41">A14</font></span></a>, <a class="ref" href="power.html#T28" title="POWER:th.28">POWER:28</a></span>;<br/><a NAME="E29:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A17</font></span>: 
<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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:47_1"><span class="lab"><font color="Green" title="E42">A15</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E30:47_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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="txt" href="#E13:47_1"><span class="lab"><font color="Green" title="E41">A14</font></span></a>, <a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></span>;<br/><span class="kw">hence </span><a NAME="E31:47_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#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:47_1"><span class="lab"><font color="Green" title="E44">A17</font></span></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_2.html#D6" title="SEQ_2:def.6">SEQ_2:def 6</a></span>;<br/>
<a NAME="E6:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A19</font></span>: 
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="seq_2.html#D7" title="SEQ_2:def.7">SEQ_2:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:47"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="asympt_0.html#T16" title="ASYMPT_0:th.16">ASYMPT_0:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<a NAME="E8:47"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="asympt_0.html#T16" title="ASYMPT_0:th.16">ASYMPT_0:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:47"/>
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="asympt_0.html#T19" title="ASYMPT_0:th.19">ASYMPT_0:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<a NAME="E10:47"/>
 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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="asympt_0.html#T19" title="ASYMPT_0:th.19">ASYMPT_0:19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:47"/>
 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 class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
