<?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="E1:31"/><i><font color="Green">E27</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="E2:31"/><i><font color="Green">E28</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="E3:31"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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#K6">Fmin</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">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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>proof </b></a><div class="add">

<a NAME="E1:31_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>(  not <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> or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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="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"><a href="radix_5.html#K6">Fmin</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="Olive">b<sub>1</sub></font> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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="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"><a href="radix_5.html#K2">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="Olive">b<sub>1</sub></font> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_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="E1:31_1_1"/><i><font color="Green">E29</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="E2:31_1_1"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:31_1_1_1_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><i><font color="Green">E32</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> = 
 <a href="radix_5.html#K1">SDMinDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#D2">RADIX_5:def 2</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_5.html#D1">RADIX_5:def 1</a></i>
;<br/><i><font color="Green">E33</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> = 
 <a href="radix_6.html#K9" target="_self">FSDMinDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_6.html#D11" target="_self">Def11</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_6.html#D10" target="_self">Def10</a></i>
;<br/> <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> = 
 <a href="radix_5.html#K5">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#D6">RADIX_5:def 6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_5.html#D5">RADIX_5:def 5</a></i>
;<br/><b>hence </b><a NAME="E5:31_1_1_1_1_1"/>
( (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> <a href="hidden.html#R1">=</a> 0 ) or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i><a class="txt" href="radix_6.html#E2:31_1_1_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="radix_6.html#E3:31_1_1_1_1_1"><i><font color="Green">E33</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:31_1_1_1_1_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1_1_1_2_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1_1_1_2"><i><font color="Green">E31</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="31_1_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:31_1_1_1_1_2_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><i><font color="Green">E33</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> = 
 <a href="radix_5.html#K1">SDMinDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#D2">RADIX_5:def 2</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_2_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D1">RADIX_5:def 1</a></i>
;<br/><i><font color="Green">E34</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> = 
 <a href="radix_6.html#K9" target="_self">FSDMinDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_6.html#D11" target="_self">Def11</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_2_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_6.html#D10" target="_self">Def10</a></i>
;<br/> <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> = 
 <a href="radix_5.html#K5">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#D6">RADIX_5:def 6</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_2_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D5">RADIX_5:def 5</a></i>
;<br/><b>hence </b><a NAME="E5:31_1_1_1_1_2_1_1_1"/>
( (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> <a href="hidden.html#R1">=</a> 0 ) or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i><a class="txt" href="radix_6.html#E2:31_1_1_1_1_2_1_1_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_6.html#E3:31_1_1_1_1_2_1_1_1"><i><font color="Green">E34</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:31_1_1_1_1_2_1_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><i><font color="Green">E33</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> = 
 <a href="radix_5.html#K1">SDMinDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#D2">RADIX_5:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E2:31_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_2_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D1">RADIX_5:def 1</a></i>
;<br/><i><font color="Green">E34</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> = 
 <a href="radix_6.html#K9" target="_self">FSDMinDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_6.html#D11" target="_self">Def11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_2_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_6.html#D10" target="_self">Def10</a></i>
;<br/> <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> = 
 <a href="radix_5.html#K5">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_5.html#D6">RADIX_5:def 6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_6.html#E1:31_1_1_1_1_2_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D5">RADIX_5:def 5</a></i>
;<br/><b>hence </b><a NAME="E5:31_1_1_1_1_2_1_1_2"/>
( (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> <a href="hidden.html#R1">=</a> 0 ) or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i><a class="txt" href="radix_6.html#E2:31_1_1_1_1_2_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_6.html#E3:31_1_1_1_1_2_1_1_2"><i><font color="Green">E34</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="E3:31_1_1_1_1_2"/>
( (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> <a href="hidden.html#R1">=</a> 0 ) or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:31_1_1"/>
( (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> <a href="hidden.html#R1">=</a> 0 ) or (  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> <a href="hidden.html#R1">=</a>  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2">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> &amp;  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6">Fmin</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> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:31_1"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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_1.html#K10">DecSD</a> 0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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#K6">Fmin</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">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>
 <b>by </b><i><a class="txt" href="radix_6.html#E1:31"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="ref" href="radix_5.html#T15">RADIX_5:15</a></i>;<br/>


</div><b>end;</b></div>
<b>then </b><span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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> 0 = 
<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#K6">Fmin</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">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>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_5.html#T6">RADIX_5:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4">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="p2">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 1,<font color="Maroon">c<sub>1</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"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2">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>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="ref" href="radix_5.html#T18">RADIX_5:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4">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="p2">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2">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"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> 1,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8">SDDec</a> <span class="p2">(<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></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_1.html#K10">DecSD</a> 1,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="ref" href="radix_5.html#T17">RADIX_5:17</a></i>
<br/>.= 
0 <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_1.html#K10">DecSD</a> 1,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_6.html#E1:31"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_5.html#T6">RADIX_5:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:31"/>
 <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" target="_self">FSDMin</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="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="radix_6.html#E1:31"><i><font color="Green">E27</font></i></a>, <a class="txt" href="radix_6.html#E2:31"><i><font color="Green">E28</font></i></a>, <a class="ref" href="radix_5.html#T9">RADIX_5:9</a></i>;<br/>


</div>
