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<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_5.html#K6" title="RADIX_5:func.6">Fmin</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> <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#K4" title="RADIX_5:func.4">SDMax</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">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="Olive" title="b2">k</font></span>)</span></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E23">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_5.html#K6" title="RADIX_5:func.6">Fmin</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> <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#K4" title="RADIX_5:func.4">SDMax</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">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="Olive" title="b2">k</font></span>)</span></span>)</span></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_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> <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#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="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> )</span><br/>

<b>assume </b><a NAME="E2:28"/><i><font color="Green" title="E24">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_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> <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#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="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></span><br/>

<a NAME="E3:28"/><b>then </b><i><font color="Green" title="E25">A3</font></i>: 
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">m</font> &amp; <font color="Maroon" title="c2">m</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/>
<a NAME="E4:28"/><i><font color="Green" title="E26">A4</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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/>
<a NAME="E5:28"/><i><font color="Green" title="E27">A5</font></i>: 
1 <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>
 
<b>by </b><i><a class="txt" href="radix_5.html#E1:28"><i><font color="Green" title="E23">A1</font></i></a>, <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="28_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E1:28"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_1"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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_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> <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#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="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></span><br/><div class="add"><i><font color="Green" title="E29">A7</font></i>:  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> = 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="radix_5.html#T4" target="_self" title="RADIX_5:th.4">Th4</a></i>
<br/>.= 
 <a href="radix_1.html#K13" title="RADIX_1:func.13">Add</a> <span class="p1">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1,<font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="txt" href="radix_5.html#E4:28"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="radix_1.html#D14" title="RADIX_1:def.14">RADIX_1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<span class="p4">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,<span class="p4">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="radix_1.html#D13" title="RADIX_1:def.13">RADIX_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,<span class="p4">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D3" title="RADIX_1:def.3">RADIX_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D3" title="RADIX_1:def.3">RADIX_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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> 
<b>by </b><i><a class="ref" href="radix_1.html#D10" title="RADIX_1:def.10">RADIX_1:def 10</a></i>
<br/>.= 
 <a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p3">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="radix_5.html#T7" target="_self" title="RADIX_5:th.7">Th7</a></i>
;<br/><a NAME="E3:28_1_1_1"/><i><font color="Green" title="E30">A8</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E3:28"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><i><font color="Green" title="E31">A9</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#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1 = 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,1
<b>by </b><i><a class="txt" href="radix_5.html#E4:28"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><b>then </b><i><font color="Green" title="E32">A10</font></i>:  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> = 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28_1_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="radix_1.html#D11" title="RADIX_1:def.11">RADIX_1:def 11</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1: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>
<b>by </b><i><a class="ref" href="radix_1.html#D10" title="RADIX_1:def.10">RADIX_1:def 10</a></i>
<br/>.= 
1

;<br/><i><font color="Green" title="E33">A11</font></i>: <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#K4" title="RADIX_5:func.4">SDMax</a> 1,<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> 1,1,<font color="Maroon" title="c3">k</font></span>)</span></span>)</span> = 
<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"><span class="p3">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<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"><span class="p2">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p5">(<span class="default"><a href="radix_5.html#K4" title="RADIX_5:func.4">SDMax</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p5">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> 1,1,<font color="Maroon" title="c3">k</font></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_2.html#T11" title="RADIX_2:th.11">RADIX_2:11</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p3">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_1"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_1"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="radix_5.html#T7" target="_self" title="RADIX_5:th.7">Th7</a></i>
<br/>.= 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#D10" title="RADIX_1:def.10">RADIX_1:def 10</a></i>
;<br/> <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span> = 
 <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> 1,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font></span>)</span>,1
<b>by </b><i><a class="ref" href="radix_5.html#T4" target="_self" title="RADIX_5:th.4">Th4</a></i>
<br/>.= 
 <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>,1
<b>by </b><i><a class="txt" href="radix_5.html#E4:28"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self" title="RADIX_5:def.6">Def6</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</a></i>
;<br/><b>hence </b><a NAME="E8:28_1_1_1"/>
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</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> <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#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="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="radix_5.html#E1:28_1_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="radix_5.html#E6:28_1_1_1"><i><font color="Green" title="E33">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="28_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2"/><i><font color="Green" title="E28">A12</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ; <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_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> <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#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="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></span><br/><div class="add"><a NAME="E2:28_1_1_2"/><i><font color="Green" title="E29">A13</font></i>: 
<font color="Maroon" title="c1">n</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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><b>then </b><i><font color="Green" title="E30">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_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>,<font color="Maroon" title="c1">n</font> = 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><i><font color="Green" title="E31">A15</font></i>: <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#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="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> = 
<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"><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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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"><span class="p2">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p5">(<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>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p5">(<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>,<font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E1:28"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_2.html#T11" title="RADIX_2:th.11">RADIX_2:11</a></i>
<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"><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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2"><i><font color="Green" title="E28">A12</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2"><i><font color="Green" title="E29">A13</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2"><i><font color="Green" title="E30">A14</font></i></a>, <a class="ref" href="radix_5.html#T8" target="_self" title="RADIX_5:th.8">Th8</a>, <a class="ref" href="radix_1.html#T21" title="RADIX_1:th.21">RADIX_1:21</a></i>
;<br/><a NAME="E5:28_1_1_2"/>
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <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> holds <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="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"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Olive" title="b1">i</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_3"><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"> ( <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> implies  <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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> )</span><br/>

<b>assume </b><a NAME="E1:28_1_1_2_3"/><i><font color="Green" title="E32">A16</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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/>

<b>then </b><i><font color="Green" title="E33">A17</font></i>:  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
 <a href="radix_1.html#K13" title="RADIX_1:func.13">Add</a> <span class="p1">(<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 class="p1">(<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>,<font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="ref" href="radix_1.html#D14" title="RADIX_1:def.14">RADIX_1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<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>,<font color="Maroon" title="c4">i</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<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>,<font color="Maroon" title="c4">i</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<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 class="p4">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p4">(<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 class="p4">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="radix_1.html#D13" title="RADIX_1:def.13">RADIX_1:def 13</a></i>
;<br/>
<a NAME="E3:28_1_1_2_3"/><i><font color="Green" title="E34">A18</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#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="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="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self" title="RADIX_5:def.6">Def6</a></i>;<br/>
<a NAME="E4:28_1_1_2_3"/><i><font color="Green" title="E35">A19</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#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>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</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="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>;<br/>
<a NAME="E5:28_1_1_2_3"/><i><font color="Green" title="E36">A20</font></i>: 
( <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <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="28_1_1_2_3_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_2_3_2_1"/>
( <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_1"/><i><font color="Green" title="E37">A21</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_1"/><b>then </b><i><font color="Green" title="E38">A22</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>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_1"/><b>then </b><i><font color="Green" title="E39">A23</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E3:28"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_1"/><b>then </b><i><font color="Green" title="E40">A24</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self" title="RADIX_5:th.2">Th2</a></i>;<br/><a NAME="E5:28_1_1_2_3_2_1_1"/><i><font color="Green" title="E41">A25</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#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>,<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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3"><i><font color="Green" title="E35">A19</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_1"><i><font color="Green" title="E38">A22</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>;<br/><a NAME="E6:28_1_1_2_3_2_1_1"/><i><font color="Green" title="E42">A26</font></i>: 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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>,<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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_1"><i><font color="Green" title="E39">A23</font></i></a>, <a class="ref" href="radix_5.html#T8" target="_self" title="RADIX_5:th.8">Th8</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_3_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_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="E1:28_1_1_2_3_2_1_1_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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 or <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 href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_1"><i><font color="Green" title="E37">A21</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_1_1_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> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> = 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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>,<font color="Maroon" title="c2">m</font>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
<br/>.= 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">m</font>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c3">k</font></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> 
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_1"><i><font color="Green" title="E40">A24</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_1"><i><font color="Green" title="E41">A25</font></i></a>, <a class="txt" href="radix_5.html#E6:28_1_1_2_3_2_1_1"><i><font color="Green" title="E42">A26</font></i></a>, <a class="txt" href="radix_5.html#E13"><i><font color="Green" title="E11">Lm2</font></i></a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="radix_1.html#T22" title="RADIX_1:th.22">RADIX_1:22</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_2_3_2_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3"><i><font color="Green" title="E34">A18</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_1"><i><font color="Green" title="E38">A22</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</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="28_1_1_2_3_2_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_1_1_1_2"/>
<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 href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E43">A27</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_1_1_1_2"/>
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_1"><i><font color="Green" title="E39">A23</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self" title="RADIX_5:th.2">Th2</a></i>;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> = 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_1_1_1_2"><i><font color="Green" title="E43">A27</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c3">k</font></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> 
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_1"><i><font color="Green" title="E40">A24</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_1"><i><font color="Green" title="E41">A25</font></i></a>, <a class="txt" href="radix_5.html#E6:28_1_1_2_3_2_1_1"><i><font color="Green" title="E42">A26</font></i></a>, <a class="txt" href="radix_5.html#E13"><i><font color="Green" title="E11">Lm2</font></i></a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="radix_1.html#T22" title="RADIX_1:th.22">RADIX_1:22</a></i>
;<br/><b>hence </b><a NAME="E7:28_1_1_2_3_2_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3"><i><font color="Green" title="E34">A18</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_1"><i><font color="Green" title="E38">A22</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</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="E8:28_1_1_2_3_2_1_1"/>
 <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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="28_1_1_2_3_2_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2"/>
<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 href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2"/><b>then </b><i><font color="Green" title="E37">A28</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>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2"/><i><font color="Green" title="E38">A29</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="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <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="28_1_1_2_3_2_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_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="E1:28_1_1_2_3_2_1_2_1_1"/>
( <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2"><i><font color="Green" title="E38">A29</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1"/><i><font color="Green" title="E39">A30</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ; <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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E40">A31</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2"><i><font color="Green" title="E37">A28</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E41">A32</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self" title="RADIX_5:th.2">Th2</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E42">A33</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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/><a NAME="E5:28_1_1_2_3_2_1_2_1_1_1"/><i><font color="Green" title="E43">A34</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E40">A31</font></i></a>, <a class="ref" href="jordan5b.html#T1" title="JORDAN5B:th.1">JORDAN5B:1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_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="E1:28_1_1_2_3_2_1_2_1_1_1_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="radix_5.html#E2:28_1_1_2_3_2_1_2"><i><font color="Green" title="E37">A28</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1"/><i><font color="Green" title="E44">A35</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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><b>then </b><i><font color="Green" title="E45">A36</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#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="c2">m</font>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#D6" target="_self" title="RADIX_5:def.6">Def6</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</a></i>
;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_1_1_1_1"/><i><font color="Green" title="E46">A37</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#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>,<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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3"><i><font color="Green" title="E35">A19</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E44">A35</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_2_1_1_1_1_1_1"/><i><font color="Green" title="E47">A38</font></i>: 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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>,<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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E44">A35</font></i></a>, <a class="ref" href="radix_5.html#T8" target="_self" title="RADIX_5:th.8">Th8</a></i>;<br/><i><font color="Green" title="E48">A39</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#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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> = 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E41">A32</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E44">A35</font></i></a>, <a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E42">A33</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E43">A34</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><a NAME="E6:28_1_1_2_3_2_1_2_1_1_1_1_1_1"/><i><font color="Green" title="E49">A40</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1_1_1_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1"/>
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E6:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E49">A40</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_1"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E5:28"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E46">A37</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E47">A38</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E48">A39</font></i></a>, <a class="ref" href="radix_5.html#T7" target="_self" title="RADIX_5:th.7">Th7</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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#T22" title="RADIX_1:th.22">RADIX_1:22</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#T10" target="_self" title="RADIX_5:th.10">Th10</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_1"/>
 <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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E45">A36</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="28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"/><i><font color="Green" title="E50">A41</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&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#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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"/><b>then </b><i><font color="Green" title="E51">A42</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"/>
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"><i><font color="Green" title="E50">A41</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self" title="RADIX_5:th.2">Th2</a></i>;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</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>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E46">A37</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E47">A38</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E48">A39</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"><i><font color="Green" title="E51">A42</font></i></a>, <a class="ref" href="radix_5.html#T8" target="_self" title="RADIX_5:th.8">Th8</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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="radix_1.html#T22" title="RADIX_1:th.22">RADIX_1:22</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E12"><i><font color="Green" title="E10">Lm1</font></i></a></i>
;<br/><b>hence </b><a NAME="E7:28_1_1_2_3_2_1_2_1_1_1_1_1_1_3_1_2"/>
 <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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_1_1_1_1"><i><font color="Green" title="E45">A36</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="E8:28_1_1_2_3_2_1_2_1_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="28_1_1_2_3_2_1_2_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2"/><i><font color="Green" title="E44">A43</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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_1_1_1_2"/><i><font color="Green" title="E45">A44</font></i>: 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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>,<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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="radix_5.html#T8" target="_self" title="RADIX_5:th.8">Th8</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2"/><i><font color="Green" title="E46">A45</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_2_1_1_1_1_1_2"/>
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="jordan5b.html#T1" title="JORDAN5B:th.1">JORDAN5B:1</a></i>;<br/><a NAME="E5:28_1_1_2_3_2_1_2_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E47">A46</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E44">A43</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:28_1_1_2_3_2_1_2_1_1_1_1_1_2"/><i><font color="Green" title="E48">A47</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1"><i><font color="Green" title="E39">A30</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self" title="RADIX_5:th.2">Th2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_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="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1"/>
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E46">A45</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E49">A48</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E50">A49</font></i>: 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E5:28"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="radix_5.html#T7" target="_self" title="RADIX_5:th.7">Th7</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#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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> = 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E6:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E48">A47</font></i></a>, <a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E47">A46</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E49">A48</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3"><i><font color="Green" title="E35">A19</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3"><i><font color="Green" title="E36">A20</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E44">A43</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E45">A44</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E50">A49</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#T10" target="_self" title="RADIX_5:th.10">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<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></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="ref" href="radix_1.html#D11" title="RADIX_1:def.11">RADIX_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<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></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E12"><i><font color="Green" title="E10">Lm1</font></i></a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/><b>hence </b><a NAME="E6:28_1_1_2_3_2_1_2_1_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3"><i><font color="Green" title="E34">A18</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E44">A43</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</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="28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E49">A50</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&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#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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E50">A51</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E49">A50</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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>
 <b>by </b><i><a class="txt" href="radix_5.html#E1:28_1_1_2_3"><i><font color="Green" title="E32">A16</font></i></a>, <a class="ref" href="radix_5.html#T2" target="_self" title="RADIX_5:th.2">Th2</a></i>;<br/><a NAME="E6:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E51">A52</font></i>: 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E50">A51</font></i></a>, <a class="ref" href="radix_5.html#T8" target="_self" title="RADIX_5:th.8">Th8</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#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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> = 
 <a href="radix_5.html#K3" title="RADIX_5:func.3">SDMaxDigit</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E6:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E48">A47</font></i></a>, <a class="ref" href="radix_5.html#D4" target="_self" title="RADIX_5:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E47">A46</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E50">A51</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</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>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</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>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3"><i><font color="Green" title="E35">A19</font></i></a>, <a class="txt" href="radix_5.html#E5:28_1_1_2_3"><i><font color="Green" title="E36">A20</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E44">A43</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E45">A44</font></i></a>, <a class="txt" href="radix_5.html#E6:28_1_1_2_3_2_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E51">A52</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E12"><i><font color="Green" title="E10">Lm1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p4">(<span class="default"><span class="p5">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<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></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="ref" href="radix_1.html#D11" title="RADIX_1:def.11">RADIX_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p3">(<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></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E12"><i><font color="Green" title="E10">Lm1</font></i></a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/><b>hence </b><a NAME="E9:28_1_1_2_3_2_1_2_1_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3"><i><font color="Green" title="E34">A18</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_1_1_1_2"><i><font color="Green" title="E44">A43</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</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="E8:28_1_1_2_3_2_1_2_1_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="E7:28_1_1_2_3_2_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="28_1_1_2_3_2_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_2"/><i><font color="Green" title="E39">A53</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E40">A54</font></i>: 
<font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <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="ref" href="nat_2.html#T10" title="NAT_2:th.10">NAT_2:10</a></i>;<br/><a NAME="E3:28_1_1_2_3_2_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E41">A55</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#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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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="ref" href="radix_1.html#D3" title="RADIX_1:def.3">RADIX_1:def 3</a></i>;<br/><a NAME="E4:28_1_1_2_3_2_1_2_1_1_2"/><i><font color="Green" title="E42">A56</font></i>: 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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 class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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="radix_5.html#E2:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E40">A54</font></i></a>, <a class="ref" href="radix_1.html#D3" title="RADIX_1:def.3">RADIX_1:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_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="E1:28_1_1_2_3_2_1_2_1_1_2_1_1"/>
( <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> or <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> )
 </span><b>by </b><i><a class="txt" href="radix_5.html#E2:28_1_1_2_3_2_1_2"><i><font color="Green" title="E37">A28</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2_3_2_1_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_2_1_1_1"/><i><font color="Green" title="E43">A57</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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_2_1_1_1"/><b>then </b>
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3"><i><font color="Green" title="E35">A19</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E39">A53</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E5:28"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E39">A53</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E41">A55</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E42">A56</font></i></a>, <a class="ref" href="radix_5.html#T7" target="_self" title="RADIX_5:th.7">Th7</a></i>
<br/>.= 
<span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p3">(<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#K3" title="XCMPLX_0:func.3">*</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>
<b>by </b><i><a class="ref" href="radix_1.html#T21" title="RADIX_1:th.21">RADIX_1:21</a>, <a class="ref" href="radix_1.html#D11" title="RADIX_1:def.11">RADIX_1:def 11</a></i>
<br/>.= 
<span class="p1">(<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> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K4" title="NAT_1: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>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="radix_5.html#T10" target="_self" title="RADIX_5:th.10">Th10</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/><b>hence </b><a NAME="E4:28_1_1_2_3_2_1_2_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3"><i><font color="Green" title="E34">A18</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_2_1_1_1"><i><font color="Green" title="E43">A57</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</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="28_1_1_2_3_2_1_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2_3_2_1_2_1_1_2_1_1_2"/><i><font color="Green" title="E43">A58</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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font></span><br/><div class="add"><a NAME="E2:28_1_1_2_3_2_1_2_1_1_2_1_1_2"/><b>then </b>
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<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>,<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="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3"><i><font color="Green" title="E35">A19</font></i></a>, <a class="ref" href="radix_5.html#D3" target="_self" title="RADIX_5:def.3">Def3</a></i>;<br/><b>then </b> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" title="RADIX_1:func.12">SD_Add_Data</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c3">k</font></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#K11" title="RADIX_1:func.11">SD_Add_Carry</a> <span class="p2">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E5:28"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="radix_5.html#E2:28_1_1_2_3"><i><font color="Green" title="E33">A17</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E39">A53</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E41">A55</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2_3_2_1_2_1_1_2"><i><font color="Green" title="E42">A56</font></i></a>, <a class="ref" href="radix_5.html#T7" target="_self" title="RADIX_5:th.7">Th7</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K11" title="RADIX_1:func.11">SD_Add_Carry</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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>
<b>by </b><i><a class="ref" href="radix_1.html#T21" title="RADIX_1:th.21">RADIX_1:21</a>, <a class="ref" href="radix_1.html#D11" title="RADIX_1:def.11">RADIX_1:def 11</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1: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>
<b>by </b><i><a class="ref" href="radix_1.html#D10" title="RADIX_1:def.10">RADIX_1:def 10</a></i>
<br/>.= 
1

;<br/><b>hence </b><a NAME="E4:28_1_1_2_3_2_1_2_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="txt" href="radix_5.html#E2:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="radix_5.html#E3:28_1_1_2_3"><i><font color="Green" title="E34">A18</font></i></a>, <a class="txt" href="radix_5.html#E1:28_1_1_2_3_2_1_2_1_1_2_1_1_2"><i><font color="Green" title="E43">A58</font></i></a>, <a class="ref" href="radix_5.html#D5" target="_self" title="RADIX_5:def.5">Def5</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="E6:28_1_1_2_3_2_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_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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="E5:28_1_1_2_3_2_1_2"/>
 <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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="E7:28_1_1_2_3"/>
 <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="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="radix_1.html#K14" title="RADIX_1:func.14">'+'</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>,<font color="Maroon" title="c4">i</font>
 ; <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="E6:28_1_1_2"/>
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</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> <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#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="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="radix_5.html#E1:28"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="radix_5.html#E4:28_1_1_2"><i><font color="Green" title="E31">A15</font></i></a>, <a class="ref" href="radix_5.html#T12" target="_self" title="RADIX_5:th.12">Th12</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="E7:28"/>
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</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> <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#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="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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
