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<span class="kw">set </span><font color="Maroon" title="c1">g</font> =  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">f</font> =  <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a> ;<br/>
<a NAME="E1:22"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a> <a href="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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</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="asympt_1.html#E18"><span class="lab"><font color="Green" title="E15">Lm11</font></span></a></span>;<br/>
<a NAME="E2:22"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a> <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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</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="txt" href="asympt_1.html#E18"><span class="lab"><font color="Green" title="E15">Lm11</font></span></a></span>;<br/>
<a NAME="E3:22"/><span class="kw">then </span>
 not  <a href="asympt_1.html#K3" title="ASYMPT_1:func.3">seq_n^</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="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="asympt_0.html#T16" title="ASYMPT_0:th.16">ASYMPT_0:16</a></span>;<br/>
<a NAME="E4:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A3</font></span>: 
 not  <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a>  <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">1 <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="asympt_0.html#T19" title="ASYMPT_0:th.19">ASYMPT_0:19</a></span>;<br/>
<a NAME="E5:22"/>
 <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</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#K3" title="ASYMPT_1:func.3">seq_n^</a> <span class="p2">(<span class="default">1 <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="#E2:22"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E17">A1</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="E6:22"/>
(  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span></span>)</span> &amp;  not  <a href="asympt_0.html#K10" title="ASYMPT_0:func.10">Big_Oh</a> <a href="asympt_1.html#K2" title="ASYMPT_1:func.2">seq_logn</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">1 <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="#E4:22"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="asympt_1.html#T4" target="_self" title="ASYMPT_1:th.4">Th4</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/>


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