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<b>let </b><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 implies  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E7">A1</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<a NAME="E2:7"/><b>then </b><i><font color="Green" title="E8">A2</font></i>: 
 <a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2
 
<b>by </b><i><a class="ref" href="radix_4.html#T1" title="RADIX_4:th.1">RADIX_4:1</a></i>;<br/>
<a NAME="E3:7"/><b>then </b><i><font color="Green" title="E9">A3</font></i>: 
 <a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,1 = 
 <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> 1,1,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="txt" href="radix_5.html#E1:7"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="radix_1.html#D9" title="RADIX_1:def.9">RADIX_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1</span>)</span></span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D8" title="RADIX_1:def.8">RADIX_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p3">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:7"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="radix_2.html#T4" title="RADIX_2:th.4">RADIX_2:4</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T10" title="NAT_2:th.10">NAT_2:10</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9" title="NEWTON:th.9">NEWTON:9</a></i>
<br/>.= 
1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c1">k</font></span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T6" title="NAT_2:th.6">NAT_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:7"/>
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E3:7"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="nat_d.html#T14" title="NAT_D:th.14">NAT_D:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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