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

<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 holds <br/> <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 holds <br/> <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<b>let </b><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 implies  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<b>assume </b><a NAME="E2:31"/><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c2">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<a NAME="E3:31"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</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" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  holds <br/>(  not <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Olive" title="b1">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Olive" title="b1">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 
<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" title="c4">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/>

<b>assume </b><a NAME="E1:31_1_1"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/>

<a NAME="E2:31_1_1"/><b>then </b><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">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" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">m</font> or <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</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" title="E31">A5</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/><div class="add"><i><font color="Green" title="E32">A6</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_5.html#K1" title="RADIX_5:func.1">SDMinDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_5.html#D2" title="RADIX_5:def.2">RADIX_5:def 2</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="radix_5.html#D1" title="RADIX_5:def.1">RADIX_5:def 1</a></i>
;<br/><i><font color="Green" title="E33">A7</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_6.html#K9" title="RADIX_6:func.9">FSDMinDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_6.html#D11" target="_self" title="RADIX_6:def.11">Def11</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="radix_6.html#D10" target="_self" title="RADIX_6:def.10">Def10</a></i>
;<br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_5.html#K5" title="RADIX_5:func.5">FminDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_5.html#D6" title="RADIX_5:def.6">RADIX_5:def 6</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="radix_5.html#D5" title="RADIX_5:def.5">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" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="#E2:31_1_1_1_1_1"><i><font color="Green" title="E32">A6</font></i></a>, <a class="txt" href="#E3:31_1_1_1_1_1"><i><font color="Green" title="E33">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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" title="E31">A8</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><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" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> or <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font> )
 </span><b>by </b><i><a class="txt" href="#E1:31_1_1_1_1_2"><i><font color="Green" title="E31">A8</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</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" title="E32">A9</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/><div class="add"><i><font color="Green" title="E33">A10</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_5.html#K1" title="RADIX_5:func.1">SDMinDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_5.html#D2" title="RADIX_5:def.2">RADIX_5:def 2</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_2_1_1_1"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="radix_5.html#D1" title="RADIX_5:def.1">RADIX_5:def 1</a></i>
;<br/><i><font color="Green" title="E34">A11</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_6.html#K9" title="RADIX_6:func.9">FSDMinDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_6.html#D11" target="_self" title="RADIX_6:def.11">Def11</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_2_1_1_1"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="radix_6.html#D10" target="_self" title="RADIX_6:def.10">Def10</a></i>
;<br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_5.html#K5" title="RADIX_5:func.5">FminDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_5.html#D6" title="RADIX_5:def.6">RADIX_5:def 6</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_2_1_1_1"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="radix_5.html#D5" title="RADIX_5:def.5">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" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="#E2:31_1_1_1_1_2_1_1_1"><i><font color="Green" title="E33">A10</font></i></a>, <a class="txt" href="#E3:31_1_1_1_1_2_1_1_1"><i><font color="Green" title="E34">A11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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" title="E32">A12</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/><div class="add"><i><font color="Green" title="E33">A13</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_5.html#K1" title="RADIX_5:func.1">SDMinDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_5.html#D2" title="RADIX_5:def.2">RADIX_5:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E2:31_1_1"><i><font color="Green" title="E30">A4</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_2_1_1_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="radix_5.html#D1" title="RADIX_5:def.1">RADIX_5:def 1</a></i>
;<br/><i><font color="Green" title="E34">A14</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_6.html#K9" title="RADIX_6:func.9">FSDMinDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_6.html#D11" target="_self" title="RADIX_6:def.11">Def11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_2_1_1_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="radix_6.html#D10" target="_self" title="RADIX_6:def.10">Def10</a></i>
;<br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_5.html#K5" title="RADIX_5:func.5">FminDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="txt" href="#E1:31_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="radix_5.html#D6" title="RADIX_5:def.6">RADIX_5:def 6</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:31_1_1_1_1_2_1_1_2"><i><font color="Green" title="E32">A12</font></i></a>, <a class="ref" href="radix_5.html#D5" title="RADIX_5:def.5">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" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 <b>by </b><i><a class="txt" href="#E2:31_1_1_1_1_2_1_1_2"><i><font color="Green" title="E33">A13</font></i></a>, <a class="txt" href="#E3:31_1_1_1_1_2_1_1_2"><i><font color="Green" title="E34">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or (  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> &amp;  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><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" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="radix_5.html#T15" title="RADIX_5:th.15">RADIX_5:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then </b><span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  = 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="radix_5.html#T6" title="RADIX_5:th.6">RADIX_5:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="radix_5.html#T18" title="RADIX_5:th.18">RADIX_5:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p3">(<span class="default"><a href="radix_5.html#K2" title="RADIX_5:func.2">SDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="radix_5.html#T17" title="RADIX_5:th.17">RADIX_5:17</a></i>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="radix_5.html#T6" title="RADIX_5:th.6">RADIX_5:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:31"/>
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_6.html#K10" title="RADIX_6:func.10">FSDMin</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="#E1:31"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="#E2:31"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="radix_5.html#T9" title="RADIX_5:th.9">RADIX_5:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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