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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:34"/>
<font color="Maroon" title="c1">m</font> <a href="radix_1.html#R1" title="RADIX_1:pred.1">is_represented_by</a> 1,<font color="Maroon" title="c2">k</font>
 ;<br/>

<a NAME="E2:34"/><b>then </b><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1
 
<b>by </b><i><a class="ref" href="radix_1.html#D12" target="_self" title="RADIX_1:def.12">Def12</a></i>;<br/>
<a NAME="E3:34"/>
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> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<b>hence </b> <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> <font color="Maroon" title="c1">m</font>,1,<font color="Maroon" title="c2">k</font></span>)</span>,1 = 
 <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c1">m</font>,1,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="ref" href="radix_1.html#D9" target="_self" title="RADIX_1:def.9">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <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="c2">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="c2">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <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="c2">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> 1
<b>by </b><i><a class="ref" href="newton.html#T9" title="NEWTON:th.9">NEWTON:9</a></i>
<br/>.= 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</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="c2">k</font></span>)</span> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1</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/>.= 
<font color="Maroon" title="c1">m</font>
<b>by </b><i><a class="txt" href="radix_1.html#E2:34"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/><br/>


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