<?xml version="1.0"?>
<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="E1:27"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<b>let </b><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="E2:27"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>2</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> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 )
 ;<br/>

<a NAME="E3:27"/><i><font color="Green">E25</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="txt" href="radix_5.html#E1:27"><i><font color="Green">E23</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E4:27"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:27_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:27_1"/><b>then </b><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<i><font color="Green">E29</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="radix_1.html#K13">Add</a> <span class="p1">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="radix_5.html#E1:27_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_1.html#D14">RADIX_1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:27"><i><font color="Green">E24</font></i></a>, <a class="txt" href="radix_5.html#E1:27_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_1.html#D13">RADIX_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12">SD_Add_Data</a> 0,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E2:27"><i><font color="Green">E24</font></i></a>, <a class="txt" href="radix_5.html#E1:27_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_5.html#T16" target="_self">Th16</a></i>
<br/>.= 
0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#T22">RADIX_1:22</a></i>
;<br/>
<a NAME="E4:27_1"/><i><font color="Green">E30</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="radix_5.html#E1:27_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_5.html#T5" target="_self">Th5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:27_1_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E2:27_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2_1_1"><b>suppose </b></a><a NAME="E1:27_1_2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:27_1_2_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_2.html#T10">NAT_2:10</a></i>;<br/><a NAME="E3:27_1_2_1_1"/><b>then </b>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="radix_1.html#D3">RADIX_1:def 3</a></i>;<br/><a NAME="E4:27_1_2_1_1"/><b>then </b>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K11">SD_Add_Carry</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="radix_5.html#E3:27_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="radix_5.html#E2:27_1_2_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_1.html#D3">RADIX_1:def 3</a></i>;<br/><b>hence </b><a NAME="E5:27_1_2_1_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="radix_5.html#E4:27_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="radix_1.html#D10">RADIX_1:def 10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2_1_2"><b>suppose </b></a><a NAME="E1:27_1_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:27_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</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_5.html#E1:27_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E3:27_1_2_1_2"/><b>then </b>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K11">SD_Add_Carry</a> 0
 <b>by </b><i><a class="txt" href="radix_5.html#E1:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E2:27"><i><font color="Green">E24</font></i></a>, <a class="txt" href="radix_5.html#E3:27_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#T16" target="_self">Th16</a></i>;<br/><b>hence </b><a NAME="E4:27_1_2_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="radix_5.html#E4:27_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="radix_1.html#D10">RADIX_1:def 10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:27_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div><b>end;</b></div>
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p5">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<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="p4">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p5">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E2:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="radix_2.html#T11">RADIX_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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">SD_Add_Carry</a> 0</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">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E2:27"><i><font color="Green">E24</font></i></a>, <a class="txt" href="radix_5.html#E3:27"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_5.html#T16" target="_self">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="radix_1.html#K14">'+'</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</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="radix_1.html#D10">RADIX_1:def 10</a></i>
;<br/>
<b>hence </b><a NAME="E6:27"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K4" target="_self">SDMax</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" target="_self">SDMin</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E4:27"><i><font color="Green">E26</font></i></a>, <a class="ref" href="radix_5.html#T12" target="_self">Th12</a></i>;<br/>


</div>
