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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</font> implies  not  <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c2">b</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:8"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not  <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c2">b</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">g</font> =  <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c2">b</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><span class="kw">set </span><font color="Maroon" title="c5">d</font> = <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span>;<br/><span class="kw">assume </span><a NAME="E1:8_1"/>
 <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c2">b</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">s</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw"> such that </span><br/><a NAME="E3:8_1"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c6">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c2">b</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E4:8_1"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
 ex <font color="Olive" title="b1">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ex <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 <br/>( <font color="Olive" title="b1">c</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>  &amp; ( for <font color="Olive" title="b3">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="b3">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b2">N</font> holds <br/>( <font color="Maroon" title="c6">s</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">n</font></span>)</span> &amp; <font color="Maroon" title="c6">s</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) ) )
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c7">c</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>, <font color="Maroon" title="c8">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> <span class="kw"> such that </span><br/><a NAME="E6:8_1"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c7">c</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">and </span><br/><a NAME="E7:8_1"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
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="c8">N</font> holds <br/>( <font color="Maroon" title="c6">s</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> &amp; <font color="Maroon" title="c6">s</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8_1"><span class="lab"><font color="Green" title="E7">A3</font></span></a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c9">N0</font> = <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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c10">N1</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c8">N</font>,<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span>;<br/><a NAME="E8:8_1"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c8">N</font>,<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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> <font color="Maroon" title="c8">N</font>
 <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="E9:8_1"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
(  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c8">N</font>,<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">N</font> or  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c8">N</font>,<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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#T16" title="XXREAL_0:th.16">XXREAL_0:16</a></span>;<br/><a NAME="E10:8_1"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c8">N</font>,<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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"><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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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/><span class="kw">reconsider </span><font color="Maroon" title="c11">N1</font> =  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c8">N</font>,<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span></span><a href="int_1.html#K2" title="INT_1:func.2">\]</a></span> 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="#E8:8_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E9:8_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">n</font> = <font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><span class="kw">set </span><font color="Maroon" title="c13">e</font> = 2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span>;<br/><a NAME="E12:8_1"/><span class="lab"><font color="Green" title="E13">A9</font></span>: 
2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></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="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></span>;<br/><a NAME="E13:8_1"/><span class="lab"><font color="Green" title="E14">A10</font></span>: 
<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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</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="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D5" title="INT_1:def.5">INT_1:def 5</a></span>;<br/><a NAME="E14:8_1"/>
 <a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font> <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,<font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="power.html#T65" title="POWER:th.65">POWER:65</a></span>;<br/><a NAME="E15:8_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A11</font></span>: 
<span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></span>;<br/><a NAME="E16:8_1"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
<font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></span>;<br/><a NAME="E17:8_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></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="txt" href="#E10:8_1"><span class="lab"><font color="Green" title="E12">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="E18:8_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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,<font color="Maroon" title="c7">c</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="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:8_1"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E19:8_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</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"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:8_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></span>;<br/><a NAME="E20:8_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c7">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:8_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></span>;<br/><a NAME="E21:8_1"/><span class="kw">then </span>
2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></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,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 <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,<font color="Maroon" title="c7">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T44" title="POWER:th.44">POWER:44</a></span>;<br/><a NAME="E22:8_1"/><span class="kw">then </span>
2 <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"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c7">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:8_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="power.html#D3" title="POWER:def.3">POWER:def 3</a></span>;<br/><a NAME="E23:8_1"/><span class="kw">then </span>
<span class="p1">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c7">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></span>;<br/><a NAME="E24:8_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:8_1"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></span>;<br/><a NAME="E25:8_1"/><span class="kw">then </span>
2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:8_1"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></span>;<br/><a NAME="E26:8_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">b</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">2 <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="asympt_1.html#E6"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a></span>;<br/><a NAME="E27:8_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A13</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="asympt_1.html#E6"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a></span>;<br/><a NAME="E28:8_1"/>
<font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c8">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:8_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E16:8_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E29:8_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c2">b</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E7:8_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a></span>;<br/><a NAME="E30:8_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">b</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">1 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K1" title="ASYMPT_1:func.1">seq_a^</a> <font color="Maroon" title="c1">a</font>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">N1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="asympt_1.html#D1" target="_self" title="ASYMPT_1:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E31:8_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:8_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="ref" href="asympt_1.html#D1" target="_self" title="ASYMPT_1:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>


</div>
