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<b>set </b><font color="Maroon" title="c2">f</font> =  <a href="asympt_1.html#K5" title="ASYMPT_1:func.5">seq_n!</a> <font color="Maroon" title="c1">a</font>;<br/>
<b>take </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="asympt_0.html#D6" title="ASYMPT_0:def.6">ASYMPT_0:def 6</a><br/>

<b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:47_1_1"/>
<font color="Maroon" title="c3">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/>

<a NAME="E2:47_1_1"/>
<span class="p1">(<span class="default"><a href="asympt_1.html#K5" title="ASYMPT_1:func.5">seq_n!</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="newton.html#K12" title="NEWTON:func.12">!</a> 
 
<b>by </b><i><a class="ref" href="asympt_1.html#D5" target="_self" title="ASYMPT_1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E3:47_1_1"/>
<span class="p1">(<span class="default"><a href="asympt_1.html#K5" title="ASYMPT_1:func.5">seq_n!</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c3">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> 
 <b>by </b><i><a class="ref" href="newton.html#T23" title="NEWTON:th.23">NEWTON:23</a></i>;<br/>


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