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

<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ;<br/>

<b>let </b><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E2:20"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="radix_1.html#R1" title="RADIX_1:pred.1">is_represented_by</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font>
 ;<br/>

<a NAME="E3:20"/>
 <a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font>
 
<b>by </b><i><a class="ref" href="radix_2.html#T14" target="_self" title="RADIX_2:th.14">Th14</a></i>;<br/>
<a NAME="E4:20"/><b>then </b>
 <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c2">m</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="radix_2.html#T13" target="_self" title="RADIX_2:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E5:20"/>
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="txt" href="radix_2.html#E1:20"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="radix_2.html#E2:20"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="radix_1.html#T25" title="RADIX_1:th.25">RADIX_1:25</a></i>;<br/>


</div>
