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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:7"/><i><font color="Green">E20</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 )
 ;<br/>

<a NAME="E2:7"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="ref" href="radix_4.html#T1">RADIX_4:1</a></i>;<br/>
<a NAME="E3:7"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:7"/><i><font color="Green">E30</font></i>: 
 <a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i/>;<br/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 1,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span>,1 = 
 <a href="radix_1.html#K9">DigitDC</a> 1,1,<font color="Maroon">k</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">1 <a href="nat_1.html#K6">mod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D8">RADIX_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K5">div</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p3">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i>, <a class="ref" href="radix_2.html#T4">RADIX_2:4</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K5">div</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 0</span>)</span></span>)</span> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T10">NAT_2:10</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K5">div</a> 1</span>)</span> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>
<br/>.= 
1 <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T6">NAT_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E6:7"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 1,<font color="Maroon">n</font>,<font color="Maroon">k</font></span>)</span>,1 <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T64">NAT_1:64</a></i>;<br/>


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