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

<a NAME="E1:19"/><i><font color="Green">E29</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" target="_self">DecSD2</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:19_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/><b>then </b><span class="p1">(<span class="default"><a href="radix_2.html#K5" target="_self">DecSD2</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font> = 
 <a href="radix_2.html#K4" target="_self">DigitDC2</a> <font color="Maroon">x</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font>
<b>by </b><i/>
<br/>.= 
 <a href="radix_1.html#K9">DigitDC</a> <font color="Maroon">x</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="radix_1.html#D8">RADIX_1:def 8</a></i>
<br/>.= 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="radix_1.html#D9">RADIX_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="radix_1.html#D3">RADIX_1:def 3</a></i>
;<br/><b>hence </b><a NAME="E3:19_1"/>
<span class="p1">(<span class="default"><a href="radix_2.html#K5" target="_self">DecSD2</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:19"/>
 <a href="radix_2.html#K5" target="_self">DecSD2</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K10">DecSD</a> <font color="Maroon">x</font>,<font color="Maroon">n</font>,<font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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