<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:34"/>
<font color="Maroon">c<sub>1</sub></font> <a href="radix_1.html#R1" target="_self">is_represented_by</a> 1,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:34"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1
 
<b>by </b><i><a class="ref" href="radix_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E3:34"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>hence </b> <a href="radix_1.html#K4" target="_self">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>1</sub></font>,1,<font color="Maroon">c<sub>2</sub></font></span>)</span>,1 = 
 <a href="radix_1.html#K9" target="_self">DigitDC</a> <font color="Maroon">c<sub>1</sub></font>,1,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="radix_1.html#D9" target="_self">Def9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 1
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T6">NAT_2:6</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="radix_1.html#E2:34"><i><font color="Green">E26</font></i></a>, <a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/><br/>


</div>
