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<b>let </b><font color="Maroon">j</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>, <font color="Maroon">k</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:10_1_2"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">j</font> <a href="seq_1.html#K2">.</a> 0 <a href="hidden.html#R1">=</a> 0 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Maroon">j</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> <a href="power.html#K4">to_power</a> <font color="Maroon">a</font> ) )
 <b>and </b><br/><a NAME="E2:10_1_2"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">k</font> <a href="seq_1.html#K2">.</a> 0 <a href="hidden.html#R1">=</a> 0 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/><font color="Maroon">k</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Olive">n</font> <a href="power.html#K4">to_power</a> <font color="Maroon">a</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_1"><b>now </b></a><div class="add"><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/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1_2_1_1"/>
( <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:10_1_2_1_1_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:10_1_2_1_1_1"/>
<font color="Maroon">j</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:10_1_2_1_1_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:10_1_2_1_1_2"/><b>then </b>
<font color="Maroon">j</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="power.html#K4">to_power</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:10_1_2_1_1_2"/>
<font color="Maroon">j</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:10_1_2"/>
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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