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

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

<b>assume </b><a NAME="E1:29"/><i><font color="Green">E23</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="E2:29"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</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/>
<a NAME="E3:29"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:29"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E5:29"/><i><font color="Green">E27</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>then </b><i><font color="Green">E28</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="radix_5.html#K5" target="_self">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<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>
<b>by </b><i><a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/>
<i><font color="Green">E29</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="radix_5.html#K7" target="_self">FmaxDigit</a> <font color="Maroon">c<sub>2</sub></font>,<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>
<b>by </b><i><a class="txt" href="radix_5.html#E5:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29"><i><font color="Green">E25</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>
;<br/>
<i><font color="Green">E30</font></i>: <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" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#K6" target="_self">Fmin</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K8" target="_self">Fmax</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</a> <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>,<font color="Maroon">c<sub>3</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">DigA</a> <span class="p5">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <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>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#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> <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>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E4:29"><i><font color="Green">E26</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#K6" target="_self">Fmin</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K8" target="_self">Fmax</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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> <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>
<b>by </b><i><a class="txt" href="radix_5.html#E6:29"><i><font color="Green">E28</font></i></a>, <a class="txt" href="radix_5.html#E7:29"><i><font color="Green">E29</font></i></a>, <a class="ref" href="radix_1.html#T21">RADIX_1:21</a></i>
;<br/>
<a NAME="E9:29"/><i><font color="Green">E31</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> <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_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="finseq_2.html#T9">FINSEQ_2:9</a></i>;<br/>
<a NAME="E10:29"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/> <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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="29_4"><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="E1:29_4"/><i><font color="Green">E32</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/>

<b>then </b><i><font color="Green">E33</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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_1.html#D13">RADIX_1:def 13</a></i>
;<br/>
<a NAME="E3:29_4"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:29_4"/><i><font color="Green">E35</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#K5" target="_self">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_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E5:29_4"/><i><font color="Green">E36</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#K7" target="_self">FmaxDigit</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_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E6:29_4"/><i><font color="Green">E37</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#K5" target="_self">FminDigit</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E7:29_4"/><i><font color="Green">E38</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="txt" href="radix_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_4_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 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> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_1"><b>suppose </b></a><a NAME="E1:29_4_2_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_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="E1:29_4_2_1_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:29_4_2_1_1_1_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>then </b><i><font color="Green">E41</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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" target="_self">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/><i><font color="Green">E42</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K7" target="_self">FmaxDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_1_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>
;<br/><i><font color="Green">E43</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_1_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
 <a href="radix_5.html#K5" target="_self">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_5.html#E9:29"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/><i><font color="Green">E44</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_1_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
 <a href="radix_5.html#K7" target="_self">FmaxDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_5.html#E9:29"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>
;<br/><i><font color="Green">E45</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="radix_5.html#K5" target="_self">FminDigit</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_1_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/> <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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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> = 
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">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:29_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_1_1_1_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4_2_1_1_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4_2_1_1_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="radix_5.html#E5:29_4_2_1_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_1.html#T22">RADIX_1:22</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#T10" target="_self">Th10</a></i>
;<br/><b>hence </b><a NAME="E8:29_4_2_1_1_1_1_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E6:29_4_2_1_1_1_1_1"><i><font color="Green">E45</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:29_4_2_1_1_1_1_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:29_4_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E41</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> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:29_4_2_1_1_1_1_2"/>
<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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:29_4_2_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E2:29"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E5:29_4_2_1_1_1_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<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> <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_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E6:29_4_2_1_1_1_1_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E2:29_4_2_1_1_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E7:29_4_2_1_1_1_1_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="radix_5.html#E6:29_4_2_1_1_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E8:29_4_2_1_1_1_1_2"/><i><font color="Green">E45</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4"><i><font color="Green">E34</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E9:29_4_2_1_1_1_1_2"/><i><font color="Green">E46</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4"><i><font color="Green">E34</font></i></a>, <a class="txt" href="radix_5.html#E5:29_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>;<br/><i><font color="Green">E47</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_5.html#K5" target="_self">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E5:29_4_2_1_1_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E7:29_4_2_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/><i><font color="Green">E48</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_5.html#K7" target="_self">FmaxDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E5:29_4_2_1_1_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E7:29_4_2_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>
;<br/><a NAME="E12:29_4_2_1_1_1_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E6:29_4"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_1_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/><b>hence </b><a NAME="E13:29_4_2_1_1_1_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E2:29_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_5.html#E8:29_4_2_1_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="radix_5.html#E9:29_4_2_1_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="radix_5.html#E10:29_4_2_1_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="radix_5.html#E11:29_4_2_1_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="radix_1.html#T21">RADIX_1:21</a>, <a class="ref" href="radix_1.html#T22">RADIX_1:22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:29_4_2_1_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_2"><b>suppose </b></a><a NAME="E1:29_4_2_1_2"/>
<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> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:29_4_2_1_2"/><b>then </b><i><font color="Green">E39</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>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4_2_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_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="E1:29_4_2_1_2_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E7:29_4"><i><font color="Green">E38</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="29_4_2_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:29_4_2_1_2_1_1_1"/><i><font color="Green">E40</font></i>: 
<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="E2:29_4_2_1_2_1_1_1"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E2:29_4_2_1_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E3:29_4_2_1_2_1_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</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="txt" href="radix_5.html#E9:29"><i><font color="Green">E31</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E4:29_4_2_1_2_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="jordan5b.html#T1">JORDAN5B:1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4_2_1_2_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_2_1_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="E1:29_4_2_1_2_1_1_1_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_5.html#E2:29_4_2_1_2"><i><font color="Green">E39</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="29_4_2_1_2_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:29_4_2_1_2_1_1_1_1_1_1"/><i><font color="Green">E44</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"><a NAME="E2:29_4_2_1_2_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E5:29_4"><i><font color="Green">E36</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>;<br/><i><font color="Green">E46</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_5.html#K5" target="_self">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4_2_1_2_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/><i><font color="Green">E47</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_5.html#K7" target="_self">FmaxDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4_2_1_2_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>
;<br/><i><font color="Green">E48</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="radix_5.html#K5" target="_self">FminDigit</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29_4"><i><font color="Green">E32</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/> <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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12">SD_Add_Data</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a>, <a class="ref" href="radix_1.html#T21">RADIX_1:21</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#T11" target="_self">Th11</a></i>
;<br/><b>hence </b><a NAME="E7:29_4_2_1_2_1_1_1_1_1_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E5:29_4_2_1_2_1_1_1_1_1_1"><i><font color="Green">E48</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_2_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:29_4_2_1_2_1_1_1_1_1_2"/><i><font color="Green">E44</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"><a NAME="E2:29_4_2_1_2_1_1_1_1_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="radix_5.html#E7:29_4"><i><font color="Green">E38</font></i></a>, <a class="ref" href="jordan5b.html#T1">JORDAN5B:1</a></i>;<br/><a NAME="E3:29_4_2_1_2_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E4:29_4_2_1_2_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E3:29"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E5:29_4_2_1_2_1_1_1_1_1_2"/>
<font color="Maroon">c<sub>4</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="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="jordan3.html#T12">JORDAN3:12</a></i>;<br/><a NAME="E6:29_4_2_1_2_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<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> <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_5.html#E4:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E7:29_4_2_1_2_1_1_1_1_1_2"/><i><font color="Green">E48</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E5:29_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>;<br/><i><font color="Green">E49</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_5.html#K5" target="_self">FminDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E6:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self">Def6</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
;<br/><i><font color="Green">E50</font></i>:  <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="radix_5.html#K7" target="_self">FmaxDigit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E6:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="radix_5.html#D8" target="_self">Def8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>
;<br/><a NAME="E10:29_4_2_1_2_1_1_1_1_1_2"/><i><font color="Green">E51</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> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/> <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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12">SD_Add_Data</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 0</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">0 <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4"><i><font color="Green">E35</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="radix_5.html#E7:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="radix_5.html#E8:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="radix_5.html#E9:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>
<br/>.= 
0 <a href="nat_1.html#K1">+</a> 0
<b>by </b><i><a class="ref" href="radix_1.html#T21">RADIX_1:21</a>, <a class="ref" href="radix_1.html#T22">RADIX_1:22</a></i>
;<br/><b>hence </b><a NAME="E12:29_4_2_1_2_1_1_1_1_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E6:29_4"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_5.html#E10:29_4_2_1_2_1_1_1_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:29_4_2_1_2_1_1_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:29_4_2_1_2_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:29_4_2_1_2_1_1_2"/><b>then </b><i><font color="Green">E40</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="E3:29_4_2_1_2_1_1_2"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4_2_1_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_2_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="E1:29_4_2_1_2_1_1_2_1_1"/>
( <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> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E2:29_4_2_1_2"><i><font color="Green">E39</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="29_4_2_1_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:29_4_2_1_2_1_1_2_1_1_1"/><i><font color="Green">E42</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"><a NAME="E2:29_4_2_1_2_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4"><i><font color="Green">E35</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:29_4_2_1_2_1_1_2_1_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E5:29_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_2_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E4:29_4_2_1_2_1_1_2_1_1_1"/><i><font color="Green">E45</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> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_2_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/> <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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12">SD_Add_Data</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 0</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">0 <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:29_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_2_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_2_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_1.html#D3">RADIX_1:def 3</a></i>
<br/>.= 
0 <a href="nat_1.html#K1">+</a> 0
<b>by </b><i><a class="ref" href="radix_1.html#T21">RADIX_1:21</a>, <a class="ref" href="radix_1.html#T22">RADIX_1:22</a></i>
;<br/><b>hence </b><a NAME="E6:29_4_2_1_2_1_1_2_1_1_1"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E6:29_4"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4_2_1_2_1_1_2_1_1_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_4_2_1_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:29_4_2_1_2_1_1_2_1_1_2"/><i><font color="Green">E42</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"><a NAME="E2:29_4_2_1_2_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4"><i><font color="Green">E35</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:29_4_2_1_2_1_1_2_1_1_2"/><i><font color="Green">E44</font></i>: 
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K8" target="_self">Fmax</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E5:29_4"><i><font color="Green">E36</font></i></a>, <a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="radix_5.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E4:29_4_2_1_2_1_1_2_1_1_2"/><i><font color="Green">E45</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> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:29_4_2_1_2_1_1_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/> <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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12">SD_Add_Data</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1">Radix</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
<b>by </b><i><a class="txt" href="radix_5.html#E2:29_4"><i><font color="Green">E33</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="radix_5.html#E2:29_4_2_1_2_1_1_2_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="radix_5.html#E3:29_4_2_1_2_1_1_2_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="radix_1.html#T21">RADIX_1:21</a>, <a class="ref" href="radix_1.html#D3">RADIX_1:def 3</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="radix_5.html#E1:29"><i><font color="Green">E23</font></i></a>, <a class="ref" href="radix_5.html#T11" target="_self">Th11</a></i>
;<br/><b>hence </b><a NAME="E6:29_4_2_1_2_1_1_2_1_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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#E1:29"><i><font color="Green">E23</font></i></a>, <a class="txt" href="radix_5.html#E6:29_4"><i><font color="Green">E37</font></i></a>, <a class="txt" href="radix_5.html#E4:29_4_2_1_2_1_1_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:29_4_2_1_2_1_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:29_4_2_1_2"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E9:29_4"/>
 <a href="radix_1.html#K4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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#K6" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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>
<b>hence </b><a NAME="E11:29"/>
 <a href="radix_1.html#K8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" target="_self">Fmin</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font></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" target="_self">Fmin</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>,<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#K8" target="_self">Fmax</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>,<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_5.html#E4:29"><i><font color="Green">E26</font></i></a>, <a class="txt" href="radix_5.html#E8:29"><i><font color="Green">E30</font></i></a>, <a class="ref" href="radix_5.html#T12" target="_self">Th12</a></i>;<br/>


</div>
