<?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> 2 &amp; <font color="Olive">b<sub>2</sub></font> <a href="radix_1.html#R1" target="_self">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" target="_self">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> <span class="p1">(<span class="default"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <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" target="_self">Radix</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:42"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_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="E1:42_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="radix_1.html#R1" target="_self">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" target="_self">is_represented_by</a> 1,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:42_1"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <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>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="radix_1.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E3:42_1"/><i><font color="Green">E35</font></i>: 
 <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <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>
 
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="radix_1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E4:42_1"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<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>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <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></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <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="xcmplx_0.html#K6">-</a> 0
 
;<br/>
<b>hence </b><a NAME="E5:42_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> <span class="p1">(<span class="default"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="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" target="_self">Radix</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>3</sub></font>,1,<font color="Maroon">c<sub>1</sub></font></span>)</span>,1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="radix_1.html#E2:42_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="radix_1.html#E3:42_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:42"/><i><font color="Green">E33</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="42_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="E1:42_2"/><i><font color="Green">E34</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="E2:42_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="E3:42_2"/><b>then </b><i><font color="Green">E35</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="E4:42_2"/><i><font color="Green">E36</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="E5:42_2"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="radix_1.html#R1" target="_self">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" target="_self">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/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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>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" target="_self">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> = <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</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" target="_self">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>9</sub></font> = <span class="p1">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" target="_self">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>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>;<br/>
<a NAME="E6:42_2"/><i><font color="Green">E38</font></i>: 
 <a href="radix_1.html#K4" target="_self">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" target="_self">DecSD</a> <font color="Maroon">c<sub>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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="radix_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E7:42_2"/>
 <a href="radix_1.html#K1" target="_self">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="radix_1.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E8:42_2"/><b>then </b>
 <a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E9:42_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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="E10:42_2"/><b>then </b><i><font color="Green">E40</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" target="_self">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" target="_self">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" target="_self">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="E11:42_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" target="_self">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" target="_self">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" target="_self">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" target="_self">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_1.html#E9:42_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="nat_1.html#T46">NAT_1:46</a></i>;<br/>
<a NAME="E12:42_2"/><b>then </b><i><font color="Green">E41</font></i>: 
( <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" target="_self">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" target="_self">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" target="_self">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" target="_self">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" target="_self">Def12</a></i>;<br/>
<a NAME="E13:42_2"/><i><font color="Green">E42</font></i>: 
 <a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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="42_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:42_2_1"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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>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="E2:42_2_1"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E3:42_2_1"/><i><font color="Green">E45</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K6" target="_self">SubDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<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_1.html#E3:42_2_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
;<br/>
<a NAME="E5:42_2_1"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E6:42_2_1"/>
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_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> holds <br/><span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="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"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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="42_2_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:42_2_1_2"/><i><font color="Green">E47</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</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_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> )
 ;<br/>

<a NAME="E2:42_2_1_2"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>11</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="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E3:42_2_1_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>11</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_1.html#E1:42_2_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E4:42_2_1_2"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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_1.html#E1:42_2_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:42_2_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_2_1_2_1"/>
( <font color="Maroon">c<sub>11</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>11</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_1.html#E3:42_2_1_2"><i><font color="Green">E49</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="42_2_1_2_1_1"><b>suppose </b></a><a NAME="E1:42_2_1_2_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>11</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="E2:42_2_1_2_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E2:42_2_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><i><font color="Green">E54</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="radix_1.html#E2:42_2_1_2_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
 <a href="radix_1.html#K6" target="_self">SubDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>11</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="radix_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K5" target="_self">DigB</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>11</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>11</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K13" target="_self">Add</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="radix_1.html#D14" target="_self">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="radix_1.html#D13" target="_self">Def13</a></i>
;<br/><i><font color="Green">E55</font></i>: <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="radix_1.html#E4:42_2_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
 <a href="radix_1.html#K6" target="_self">SubDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_1.html#E3:42_2_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="radix_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K5" target="_self">DigB</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K13" target="_self">Add</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E3:42_2_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="radix_1.html#D14" target="_self">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_1.html#E3:42_2_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="radix_1.html#D13" target="_self">Def13</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2_1_2_1_1_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_1_2_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_2_1_2_1_1_3_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_1_2_1_1_3_1_1"><b>suppose </b></a><a NAME="E1:42_2_1_2_1_1_3_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then </b><i><font color="Green">E57</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E3:42_2_1_2_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1_3_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D3" target="_self">Def3</a>, <a class="ref" href="radix_1.html#T21" target="_self">Th21</a></i>
;<br/><span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E4:42_2_1_2_1_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="radix_1.html#E1:42_2_1_2_1_1_3_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1_3_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D3" target="_self">Def3</a>, <a class="ref" href="radix_1.html#T21" target="_self">Th21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></a></i>
;<br/><b>hence </b><a NAME="E4:42_2_1_2_1_1_3_1_1"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font>
 <b>by </b><i><a class="txt" href="radix_1.html#E2:42_2_1_2_1_1_3_1_1"><i><font color="Green">E57</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_1_2_1_1_3_1_2"><b>suppose </b></a><a NAME="E1:42_2_1_2_1_1_3_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:42_2_1_2_1_1_3_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="jordan3.html#T12">JORDAN3:12</a></i>;<br/><a NAME="E3:42_2_1_2_1_1_3_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="radix_1.html#E2:42_2_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E4:42_2_1_2_1_1_3_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1 <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_1.html#E5:42_2_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="radix_1.html#E2:42_2_1_2_1_1_3_1_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="radix_1.html#E4:42_2_1_2_1_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E4:42_2_1_2_1_1_3_1_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>11</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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <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_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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 class="p5">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E4:42_2_1_2_1_1_3_1_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></a></i>
;<br/><b>hence </b><a NAME="E6:42_2_1_2_1_1_3_1_2"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font>
 <b>by </b><i><a class="txt" href="radix_1.html#E3:42_2_1_2_1_1"><i><font color="Green">E54</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:42_2_1_2_1_1"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_1_2_1_2"><b>suppose </b></a><a NAME="E1:42_2_1_2_1_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>11</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"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="radix_1.html#K6" target="_self">SubDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="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_1.html#E4:42_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="radix_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</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_1.html#E4:42_2_1_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="radix_1.html#E1:42_2_1_2_1_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E3:42_2_1_2_1_2"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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>11</sub></font>
 <b>by </b><i><a class="txt" href="radix_1.html#E1:42_2_1_2_1_2"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E7:42_2_1"/>
 <a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#E5:42_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:42_2"/><i><font color="Green">E43</font></i>: 
 <a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> is    <a href="trees_4.html#M1">FinSequence</a> of  <a href="wsierp_1.html#K6">INT</a> 
 
;<br/>
<i><font color="Green">E44</font></i>:  <a href="radix_1.html#K6" target="_self">SubDigit</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><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_1.html#K5" target="_self">DigB</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K5" target="_self">DigB</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
 <a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" target="_self">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> = 
 <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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_1.html#K6" target="_self">SubDigit</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="radix_1.html#E13:42_2"><i><font color="Green">E42</font></i></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" target="_self">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#K5" target="_self">DigB</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E14:42_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="radix_1.html#E15:42_2"><i><font color="Green">E44</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="radix_1.html#K4" target="_self">DigA</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K13" target="_self">Add</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E4:42_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="radix_1.html#D14" target="_self">Def14</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#K12" target="_self">SD_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E4:42_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="radix_1.html#D13" target="_self">Def13</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#K12" target="_self">SD_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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#K12" target="_self">SD_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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="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#K12" target="_self">SD_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E3:42_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></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#K12" target="_self">SD_Add_Data</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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 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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E3:42_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_1.html#E41"><i><font color="Green">Lemma27</font></i></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#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="radix_1.html#K7" target="_self">DigitSD</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_1.html#E6:42_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="radix_1.html#T27" target="_self">Th27</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#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</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_1.html#K1" target="_self">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="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</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#K11" target="_self">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<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_1.html#K4" target="_self">DigA</a> <span class="p0">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" target="_self">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" target="_self">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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</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"><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" target="_self">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" target="_self">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_1.html#E1:42_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="radix_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_1.html#E12:42_2"><i><font color="Green">E41</font></i></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#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</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_1.html#K1" target="_self">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="xcmplx_0.html#K2">+</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" target="_self">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"><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" target="_self">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>

;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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 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#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</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_1.html#K1" target="_self">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="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <span class="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"><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" target="_self">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"><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" target="_self">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>

<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#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</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_1.html#K1" target="_self">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="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</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" target="_self">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="p5">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <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"><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" target="_self">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"><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" target="_self">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="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#K12" target="_self">SD_Add_Data</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</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_1.html#K1" target="_self">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="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#K11" target="_self">SD_Add_Carry</a> <span class="p0">(<span class="default"><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" target="_self">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#K3">div</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></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="nat_1.html#K4">mod</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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"><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" target="_self">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>

<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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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#K3">div</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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>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" target="_self">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> <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" target="_self">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>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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>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" target="_self">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K3">div</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <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" target="_self">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>

<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_1.html#E9:42_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="radix_1.html#E10:42_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nat_1.html#T47">NAT_1:47</a></i>
;<br/>
<b>hence </b><a NAME="E18:42_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> <span class="p1">(<span class="default"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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="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" target="_self">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_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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></span>)</span>
 <b>by </b><i><a class="txt" href="radix_1.html#E5:42_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_1.html#E6:42_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="radix_1.html#T27" target="_self">Th27</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:42"/>
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_1.html#E1:42"><i><font color="Green">E32</font></i></a>, <a class="txt" href="radix_1.html#E2:42"><i><font color="Green">E33</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:42"/>
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> 2 &amp; <font color="Olive">b<sub>3</sub></font> <a href="radix_1.html#R1" target="_self">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" target="_self">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> <span class="p1">(<span class="default"><a href="radix_1.html#K8" target="_self">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <a href="radix_1.html#K14" target="_self">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" target="_self">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> <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" target="_self">Radix</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" target="_self">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>,<font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/>


</div>
