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<b>let </b><font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">k</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:46_1_2"/><i><font color="Green" title="E32">A2</font></i>: 
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>  holds  <font color="Maroon" title="c2">j</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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>and </b><br/><a NAME="E2:46_1_2"/><i><font color="Green" title="E33">A3</font></i>: 
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>  holds  <font color="Maroon" title="c3">k</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">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>thus </b><font color="Maroon" title="c2">j</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="txt" href="asympt_1.html#E1:46_1_2"><i><font color="Green" title="E32">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">k</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="asympt_1.html#E2:46_1_2"><i><font color="Green" title="E33">A3</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:46_1_2"/>
<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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