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<b>set </b><font color="Maroon">f</font> =  <a href="asympt_1.html#K3" target="_self">seq_n^</a> 1;<br/>
<b>set </b><font color="Maroon">g</font> =  <a href="asympt_1.html#K4" target="_self">seq_const</a> 1;<br/>
<b>take </b>
2
; <i><font color="Red">:: according to </font></i><a class="ref" href="asympt_0.html#D6">ASYMPT_0:def 6</a><br/>

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:116"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 ;<br/>

<a NAME="E2:116"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<i><font color="Green">E51</font></i>: <span class="p1">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> = 
<font color="Maroon">n</font> <a href="series_1.html#K3">to_power</a> 1
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
;<br/>
<a NAME="E4:116"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><a href="asympt_1.html#K4" target="_self">seq_const</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> 1</span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K4" target="_self">seq_const</a> 1</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> 1</span>)</span> <a href="seq_1.html#K9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17">-</a> <span class="p3">(<span class="default"><a href="asympt_1.html#K4" target="_self">seq_const</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="seq_1.html#T15">SEQ_1:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> 1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seq_1.html#K17">-</a> <span class="p3">(<span class="default"><a href="asympt_1.html#K4" target="_self">seq_const</a> 1</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T11">SEQ_1:11</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>
<b>by </b><i>, , <a class="ref" href="seq_1.html#T14">SEQ_1:14</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="real_1.html#K5">-</a> 1

;<br/>
<b>hence </b><a NAME="E6:116"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="asympt_1.html#K3" target="_self">seq_n^</a> 1</span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><a href="asympt_1.html#K4" target="_self">seq_const</a> 1</span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/>


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