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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">n</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">  <a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">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="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span><br/>

<a NAME="E1:19"/><i><font color="Green" title="E15">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E2:19"/><i><font color="Green" title="E16">X</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">j</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">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> implies <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font> )</span><br/><b>assume </b><a NAME="E1:19_1"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font></span><br/><b>then </b><span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">j</font> = 
 <a href="radix_2.html#K4" title="RADIX_2:func.4">DigitDC2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c4">j</font>,<font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="ref" href="radix_2.html#D5" target="_self" title="RADIX_2:def.5">Def5</a>, <a class="txt" href="#E2:19"><i><font color="Green" title="E16">X</font></i></a></i>
<br/>.= 
 <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c4">j</font>,<font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="ref" href="radix_1.html#D8" title="RADIX_1:def.8">RADIX_1:def 8</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_1.html#K10" title="RADIX_1:func.10">DecSD</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span>,<font color="Maroon" title="c4">j</font>
<b>by </b><i><a class="txt" href="#E1:19_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="#E2:19"><i><font color="Green" title="E16">X</font></i></a>, <a class="ref" href="radix_1.html#D9" title="RADIX_1:def.9">RADIX_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</font>
<b>by </b><i><a class="txt" href="#E1:19_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="#E2:19"><i><font color="Green" title="E16">X</font></i></a>, <a class="ref" href="radix_1.html#D3" title="RADIX_1:def.3">RADIX_1:def 3</a></i>
;<br/><b>hence </b><a NAME="E3:19_1"/>
<span class="p1">(<span class="default"><a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">j</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="E4:19"/>
 <a href="radix_2.html#K5" title="RADIX_2:func.5">DecSD2</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">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="c1">x</font>,<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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