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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Olive">b<sub>2</sub></font> <a href="radix_1.html#R1">is_represented_by</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="radix_1.html#R1">is_represented_by</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_3.html#K14">SDSub2IntOut</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Olive">b<sub>2</sub></font>,<font color="Maroon">a<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Olive">b<sub>3</sub></font>,<font color="Maroon">a<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:14"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:14_1"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="radix_1.html#R1">is_represented_by</a> 1,<font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="radix_1.html#R1">is_represented_by</a> 1,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:14_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<a NAME="E4:14_1"/><i><font color="Green">E17</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>then </b><i><font color="Green">E18</font></i>:  <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1 = 
 <a href="radix_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="radix_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E4:14_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="radix_4.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,0</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,0</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D5">RADIX_3:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 0</span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D5">RADIX_3:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="radix_3.html#T17">RADIX_3:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <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>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D4">RADIX_3:def 4</a></i>
;<br/>
<a NAME="E6:14_1"/>
2 <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> 1
 
;<br/>
<a NAME="E7:14_1"/><b>then </b><i><font color="Green">E19</font></i>: 
2 <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E8:14_1"/><i><font color="Green">E20</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>then </b><i><font color="Green">E21</font></i>:  <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,2 = 
 <a href="radix_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="radix_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default">2 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default">2 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E8:14_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_4.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,2</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E7:14_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="radix_4.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="radix_4.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="radix_3.html#D4">RADIX_3:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="radix_4.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font>

;<br/>
<i><font color="Green">E22</font></i>: <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E4:14_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="radix_3.html#D11">RADIX_3:def 11</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>1</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> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</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>1</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>
<br/>.= 
 <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,1 as    <a href="subset_1.html#M2">Element</a> of  <a href="wsierp_1.html#K6">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 = 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,2,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E8:14_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_3.html#D11">RADIX_3:def 11</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>1</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <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_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,2</span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,2</span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E7:14_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="newton.html#T10">NEWTON:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,2</span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,2</span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="wsierp_1.html#K6">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<a NAME="E14:14_1"/><i><font color="Green">E24</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E15:14_1"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E4:14_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E16:14_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="radix_4.html#E10:14_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E17:14_1"/>
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E8:14_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_4.html#E14:14_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E18:14_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="radix_4.html#E12:14_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E19:14_1"/><b>then </b>
 <a href="radix_3.html#K13">SDSub2INT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E14:14_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="radix_4.html#E16:14_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>
<a NAME="E20:14_1"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T107">RVSUM_1:107</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>, <font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E5:14_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="radix_4.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="radix_4.html#E2:14_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="radix_4.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font>

;<br/>
<b>then </b><font color="Maroon">c<sub>7</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E9:14_1"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 0

;<br/>
<b>hence </b><a NAME="E25:14_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_3.html#K14">SDSub2IntOut</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="radix_4.html#E20:14_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="radix_3.html#D12">RADIX_3:def 12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:14"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:14_2"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>1</sub></font>] )
 ;<br/>

<a NAME="E2:14_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
;<br/>
<a NAME="E3:14_2"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>1</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>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/>
<a NAME="E4:14_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E5:14_2"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="radix_1.html#R1">is_represented_by</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="radix_1.html#R1">is_represented_by</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E6:14_2"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E7:14_2"/>
 <a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="power.html#T39">POWER:39</a></i>;<br/>
<a NAME="E8:14_2"/><b>then </b>
 <a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/>
<a NAME="E9:14_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/>
<a NAME="E10:14_2"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>;<br/>
<a NAME="E11:14_2"/>
( <font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="radix_4.html#E9:14_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="nat_1.html#T46">NAT_1:46</a></i>;<br/>
<a NAME="E12:14_2"/><b>then </b>
( <font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="radix_1.html#R1">is_represented_by</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="radix_1.html#R1">is_represented_by</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="radix_1.html#D12">RADIX_1:def 12</a></i>;<br/>
<b>then </b><i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="radix_3.html#K14">SDSub2IntOut</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a></i>
<br/>.= 
 <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D12">RADIX_3:def 12</a></i>
;<br/>
<a NAME="E14:14_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E4:14_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="finseq_2.html#T9">FINSEQ_2:9</a></i>;<br/>
<a NAME="E15:14_2"/><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="wsierp_1.html#K6">INT</a>  =  <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="trees_4.html#M1">FinSequence</a> of  <a href="wsierp_1.html#K6">INT</a> <b> such that </b><br/><a NAME="E17:14_2"/><i><font color="Green">E26</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E18:14_2"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="trees_4.html#M1">FinSequence</a> of  <a href="wsierp_1.html#K6">INT</a> <b> such that </b><br/><a NAME="E20:14_2"/><i><font color="Green">E28</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E21:14_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</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> holds <br/><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="wsierp_1.html#K6">INT</a>  =  <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="trees_4.html#M1">FinSequence</a> of  <a href="wsierp_1.html#K6">INT</a> <b> such that </b><br/><a NAME="E23:14_2"/><i><font color="Green">E30</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E24:14_2"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</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> holds <br/><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i>
<a NAME="E25:14_2"/><i><font color="Green">E32</font></i>: 
 <a href="radix_3.html#K13">SDSub2INT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:14_2_2"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="radix_4.html#E17:14_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E2:14_2_2"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E3:14_2_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:14_2_2_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:14_2_2_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:14_2_2_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>12</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_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_2_2_1_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_2_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_2.html#T8">FINSEQ_2:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:14_2_2_1_1_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:14_2_2_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="radix_4.html#E17:14_2"><i><font color="Green">E26</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"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E18:14_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_2_1_1_1_1"><i><font color="Green">E37</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_2_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="radix_3.html#D11">RADIX_3:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E4:14_2_2_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:14_2_2_1_1_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:14_2_2_1_1_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>12</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_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_2_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E17:14_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_2_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_2_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="radix_3.html#D11">RADIX_3:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2_2_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_2_1_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E4:14_2_2_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:14_2_2_1"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:14_2_2"/>
 <a href="radix_3.html#K13">SDSub2INT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="radix_4.html#E1:14_2_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E26:14_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:14_2_3"/><i><font color="Green">E34</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="radix_4.html#E20:14_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E2:14_2_3"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:14_2_3_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<a NAME="E2:14_2_3_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E17:14_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_3_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_3_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_2_3_1_1_1"/>
( <font color="Maroon">c<sub>12</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> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_3_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_2.html#T8">FINSEQ_2:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_3_1_1_1_1"><b>suppose </b></a><a NAME="E1:14_2_3_1_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>12</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/><div class="add"><a NAME="E2:14_2_3_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="radix_4.html#E20:14_2"><i><font color="Green">E28</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"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E21:14_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_3_1_1_1_1"><i><font color="Green">E36</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E18:14_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_3_1"><i><font color="Green">E35</font></i></a></i>
;<br/><b>hence </b><a NAME="E4:14_2_3_1_1_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_3_1_1_1_2"><b>suppose </b></a><a NAME="E1:14_2_3_1_1_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E20:14_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E18:14_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_3_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_3_1_1_1_2"><i><font color="Green">E36</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:14_2_3_1_1_1_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:14_2_3_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:14_2_3"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="radix_4.html#E17:14_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E27:14_2"/><i><font color="Green">E34</font></i>: 
 <a href="radix_3.html#K13">SDSub2INT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_4"><b>proof </b></a><div class="add">

<a NAME="E1:14_2_4"/><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="radix_4.html#E23:14_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E2:14_2_4"/><i><font color="Green">E36</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E3:14_2_4"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:14_2_4_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:14_2_4_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_4"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:14_2_4_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>12</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_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_4"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_4_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_4_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_2_4_1_1_1"/>
( <font color="Maroon">c<sub>12</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> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_4_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_2.html#T8">FINSEQ_2:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_4_1_1_1_1"><b>suppose </b></a><a NAME="E1:14_2_4_1_1_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>12</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/><div class="add"><a NAME="E2:14_2_4_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="radix_4.html#E23:14_2"><i><font color="Green">E30</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"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E24:14_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_4_1_1_1_1"><i><font color="Green">E39</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_4_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="radix_3.html#D11">RADIX_3:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2_4_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E4:14_2_4_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_2_4_1_1_1_2"><b>suppose </b></a><a NAME="E1:14_2_4_1_1_1_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:14_2_4_1_1_1_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>12</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_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_4_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E23:14_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_4_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E2:14_2_4_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_4_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="radix_3.html#D11">RADIX_3:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2_4_1_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_4_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E4:14_2_4_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:14_2_4_1"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:14_2_4"/>
 <a href="radix_3.html#K13">SDSub2INT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K4">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="radix_4.html#E1:14_2_4"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_4"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E28:14_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_5"><b>proof </b></a><div class="add">

<a NAME="E1:14_2_5"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font> holds <br/><font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:14_2_5_1"/><i><font color="Green">E36</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font> )
 ;<br/>

<a NAME="E2:14_2_5_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>12</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>
 
<b>by </b><i><a class="txt" href="radix_4.html#E23:14_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:14_2_5_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="radix_4.html#E23:14_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="radix_4.html#E1:14_2_5_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E4:14_2_5_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2_5_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E5:14_2_5_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2_5_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E6:14_2_5_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2_5_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E21:14_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_5_1"><i><font color="Green">E37</font></i></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>12</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_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</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>12</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_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</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>12</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_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E6:14_2_5_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="radix_4.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>12</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_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_5_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="radix_4.html#T8" target="_self">Th8</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>12</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_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E4:14_2_5_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="radix_4.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>12</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_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</a></i>
<br/>.= 
 <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E24:14_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="radix_4.html#E2:14_2_5_1"><i><font color="Green">E37</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E8:14_2_5_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:14_2_5"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="radix_4.html#E20:14_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_4.html#E23:14_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>
<i><font color="Green">E36</font></i>:  <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E25:14_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rvsum_1.html#T104">RVSUM_1:104</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E26:14_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_4.html#E28:14_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="rvsum_1.html#T104">RVSUM_1:104</a></i>
;<br/>
<a NAME="E30:14_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E13:14_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_4.html#E27:14_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rvsum_1.html#T104">RVSUM_1:104</a></i>;<br/>
<a NAME="E31:14_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<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="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font>;<br/>
<i><font color="Green">E38</font></i>:  <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E15:14_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_4.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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_4.html#E15:14_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_4.html#D1" target="_self">Def1</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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

;<br/>
<i><font color="Green">E39</font></i>:  <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E14:14_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="radix_4.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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_4.html#E14:14_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="radix_4.html#D1" target="_self">Def1</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D4">RADIX_3:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

;<br/>
<i><font color="Green">E40</font></i>:  <a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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_3.html#K11">DigB_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D10">RADIX_3:def 10</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"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <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_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D9">RADIX_3:def 9</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_4.html#K1" target="_self">SDSubAddDigit</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E4:14_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="radix_4.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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E4:14_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_4.html#D1" target="_self">Def1</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="radix_4.html#T5" target="_self">Th5</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="radix_4.html#T5" target="_self">Th5</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_3.html#T21">RADIX_3:21</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_3.html#T21">RADIX_3:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> =  <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>19</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<i><font color="Green">E41</font></i>:  <a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <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="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_3.html#D4">RADIX_3:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <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="nat_1.html#K2">*</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="radix_4.html#T2" target="_self">Th2</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> = <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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<i><font color="Green">E42</font></i>:  <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E29:14_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_4.html#E31:14_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_4.html#E32:14_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="radix_4.html#E33:14_2"><i><font color="Green">E39</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><a href="radix_3.html#K12">SDSub2INTDigit</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p5">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

;<br/>
<a NAME="E37:14_2"/><i><font color="Green">E43</font></i>: 
<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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p0">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="radix_3.html#D4">RADIX_3:def 4</a></i>;<br/>
<i><font color="Green">E44</font></i>:  <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="radix_3.html#K9">SD2SDSubDigitS</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E15:14_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_3.html#D8">RADIX_3:def 8</a></i>
<br/>.= 
 <a href="radix_3.html#K8">SD2SDSubDigit</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_4.html#E15:14_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_3.html#D7">RADIX_3:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="radix_3.html#D6">RADIX_3:def 6</a></i>
<br/>.= 
 <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<i><font color="Green">E45</font></i>:  <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="radix_3.html#K9">SD2SDSubDigitS</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E15:14_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_3.html#D8">RADIX_3:def 8</a></i>
<br/>.= 
 <a href="radix_3.html#K8">SD2SDSubDigit</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="radix_4.html#E15:14_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_3.html#D7">RADIX_3:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="radix_3.html#D6">RADIX_3:def 6</a></i>
<br/>.= 
 <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<b>then </b><i><font color="Green">E46</font></i>: <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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K6">SDSub_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p4">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="radix_4.html#E37:14_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="radix_4.html#E38:14_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_4.html#T2" target="_self">Th2</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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E38:14_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="radix_4.html#E39:14_2"><i><font color="Green">E45</font></i></a></i>
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>, <font color="Maroon">c<sub>24</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7">DigA_SDSub</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>, <font color="Maroon">c<sub>25</sub></font> = <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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <font color="Maroon">c<sub>26</sub></font> = <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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <font color="Maroon">c<sub>27</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <font color="Maroon">c<sub>28</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <font color="Maroon">c<sub>29</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>, <font color="Maroon">c<sub>30</sub></font> = <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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<i><font color="Green">E47</font></i>:  <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E34:14_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="radix_4.html#E35:14_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="radix_4.html#E36:14_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="radix_4.html#E40:14_2"><i><font color="Green">E46</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>27</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_4.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>30</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>28</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>30</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E1:14_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="radix_4.html#E6:14_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="radix_4.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>26</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>26</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="radix_4.html#E3"><i><font color="Green">Lemma3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>3</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>28</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_4.html#E3:14_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="radix_4.html#E3"><i><font color="Green">Lemma3</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p5">(<span class="default"><span class="p0">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>

;<br/>
<a NAME="E43:14_2"/>
<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <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> <font color="Maroon">c<sub>1</sub></font></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="nat_1.html#K3">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">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="radix_1.html#T27">RADIX_1:27</a></i>;<br/>
<a NAME="E44:14_2"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="radix_3.html#K13">SDSub2INT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E5:14_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="radix_4.html#E10:14_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="radix_4.html#E42:14_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="radix_1.html#T27">RADIX_1:27</a></i>;<br/>
<a NAME="E45:14_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default"><span class="p4">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_4.html#E9:14_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>;<br/>
<b>hence </b><a NAME="E46:14_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_3.html#K14">SDSub2IntOut</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="radix_4.html#E44:14_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="radix_3.html#D12">RADIX_3:def 12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:14"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S9">NAT_1:sch 9</a>(<a class="txt" href="radix_4.html#E1:14"><i><font color="Green">E14</font></i></a>, <a class="txt" href="radix_4.html#E2:14"><i><font color="Green">E15</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:14"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 holds <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Olive">b<sub>3</sub></font> <a href="radix_1.html#R1">is_represented_by</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="radix_1.html#R1">is_represented_by</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_3.html#K14">SDSub2IntOut</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="radix_4.html#K2" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/>


</div>
