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

<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 &amp; <font color="Maroon" title="c1">f</font> <a href="radix_6.html#R1" title="RADIX_6:pred.1">needs_digits_of</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font> implies <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <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> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:15"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">and </span><br/><a NAME="E2:15"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2
 <span class="kw">and </span><br/><a NAME="E3:15"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c1">f</font> <a href="radix_6.html#R1" title="RADIX_6:pred.1">needs_digits_of</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <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> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span></span><br/>

<a NAME="E4:15"/>
 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="c2">m</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_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<font color="Olive" title="b1">i</font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="c2">m</font> implies  <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> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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><br/>

<span class="kw">assume </span><a NAME="E1:15_1"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<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="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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><br/>

<a NAME="E2:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:15_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_1"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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><br/><div class="add"><a NAME="E2:15_1_1_1_1"/><span class="kw">then </span>
 <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> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="radix_6.html#T6" target="_self" title="RADIX_6:th.6">Th6</a></span>;<br/><a NAME="E3:15_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A7</font></span>: 
 <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> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <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 class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T7" title="INT_1:th.7">INT_1:7</a></span>;<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="c2">m</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>) = 
 <a href="radix_5.html#K5" title="RADIX_5:func.5">FminDigit</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="radix_5.html#D6" title="RADIX_5:def.6">RADIX_5:def 6</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E1:15_1_1_1_1"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="radix_5.html#D5" title="RADIX_5:def.5">RADIX_5:def 5</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:15_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_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15_1_1_1_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:15_1_1_1_2"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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><br/><div class="add"> <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="c2">m</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>,<font color="Maroon" title="c4">i</font>) = 
 <a href="radix_5.html#K5" title="RADIX_5:func.5">FminDigit</a> (<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c4">i</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="radix_5.html#D6" title="RADIX_5:def.6">RADIX_5:def 6</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E1:15_1_1_1_2"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="radix_5.html#D5" title="RADIX_5:def.5">RADIX_5:def 5</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:15_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_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="radix_6.html#T5" target="_self" title="RADIX_6:th.5">Th5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:15_1"/>
 <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> (<font color="Maroon" title="c1">f</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="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p1">(<span class="default"><a href="radix_5.html#K6" title="RADIX_5:func.6">Fmin</a> (<font color="Maroon" title="c2">m</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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E5:15"/><span class="kw">then </span>
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <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="c2">m</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="radix_5.html#T13" title="RADIX_5:th.13">RADIX_5:13</a></span>;<br/>
<a NAME="E6:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A9</font></span>: 
 <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <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> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="radix_6.html#T1" target="_self" title="RADIX_6:th.1">Th1</a></span>;<br/>
<a NAME="E7:15"/>
<font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="radix_6.html#D7" target="_self" title="RADIX_6:def.7">Def7</a></span>;<br/>
<a NAME="E8:15"/><span class="kw">then </span>
<font color="Maroon" title="c1">f</font> <a href="radix_1.html#R1" title="RADIX_1:pred.1">is_represented_by</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="radix_1.html#D12" title="RADIX_1:def.12">RADIX_1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:15"/>
<font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <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> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="ref" href="radix_1.html#T22" title="RADIX_1:th.22">RADIX_1:22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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