<?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>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="radix_1.html#K3">-SD</a> </span>)</span>;<br/>





<b>assume </b><a NAME="E1:17"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><i><font color="Green">E14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>then </b><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> = 
 <a href="radix_1.html#K4">DigA</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="radix_2.html#E1:17"><i><font color="Green">E13</font></i></a>, <a class="ref" href="radix_1.html#D3">RADIX_1:def 3</a></i>
<br/>.= 
 <a href="radix_1.html#K5">DigB</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="radix_1.html#D4">RADIX_1:def 4</a></i>
;<br/><b>hence </b><a NAME="E3:17_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K5">DigB</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/></div><b>end;</b></div>
<a NAME="E3:17"/><i><font color="Green">E15</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_2.html#K2" target="_self">DigitSD2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></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="17_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:17_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:17_2"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_2.html#K2" target="_self">DigitSD2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="radix_2.html#E3:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><a href="radix_2.html#K2" target="_self">DigitSD2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><a href="radix_2.html#K2" target="_self">DigitSD2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
 <a href="radix_2.html#K1" target="_self">SubDigit2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_2.html#E1:17_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="radix_2.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1">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"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1">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"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K5">DigB</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_2.html#E2:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="radix_2.html#E1:17_2"><i><font color="Green">E16</font></i></a></i>
<br/>.= 
 <a href="radix_1.html#K6">SubDigit</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="radix_1.html#D5">RADIX_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="radix_2.html#E1:17_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="radix_1.html#D6">RADIX_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="radix_2.html#E2:17_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E4:17_2"/>
<span class="p1">(<span class="default"><a href="radix_2.html#K2" target="_self">DigitSD2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:17"/>
 <a href="radix_2.html#K2" target="_self">DigitSD2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K7">DigitSD</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="radix_2.html#E3:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


</div>
