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

<b>let </b><font color="Maroon" title="c4">k1</font>, <font color="Maroon" title="c5">k2</font> be   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Maroon" title="c2">n</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a> </span>)</span>; <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">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">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <font color="Maroon" title="c4">k1</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font> ) &amp; ( 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">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <font color="Maroon" title="c5">k2</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font> ) implies <font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:28_1_2"/><i><font color="Green" title="E18">A5</font></i>: 
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">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <font color="Maroon" title="c4">k1</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font>
 <b>and </b><br/><a NAME="E2:28_1_2"/><i><font color="Green" title="E19">A6</font></i>: 
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">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <font color="Maroon" title="c5">k2</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font></span><br/>

<a NAME="E3:28_1_2"/><i><font color="Green" title="E20">A7</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">k1</font> <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> <font color="Maroon" title="c5">k2</font> <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="E4:28_1_2"/><i><font color="Green" title="E21">X</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">k1</font> <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="radix_1.html#E3:28_1_2"><i><font color="Green" title="E20">A7</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="28_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">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="c6">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> <font color="Maroon" title="c4">k1</font> implies <font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> )</span><br/><b>assume </b><a NAME="E1:28_1_2_1"/><i><font color="Green" title="E22">A8</font></i>: 
<font color="Maroon" title="c6">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> <font color="Maroon" title="c4">k1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font></span><br/><b>then </b><font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> = 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c6">j</font>
<b>by </b><i><a class="ref" href="radix_1.html#D3" target="_self" title="RADIX_1:def.3">Def3</a>, <a class="txt" href="radix_1.html#E4:28_1_2"><i><font color="Green" title="E21">X</font></i></a></i>
<br/>.= 
 <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="txt" href="radix_1.html#E1:28_1_2"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="radix_1.html#E1:28_1_2_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="radix_1.html#E4:28_1_2"><i><font color="Green" title="E21">X</font></i></a></i>
<br/>.= 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <font color="Maroon" title="c5">k2</font>,<font color="Maroon" title="c6">j</font>
<b>by </b><i><a class="txt" href="radix_1.html#E2:28_1_2"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="radix_1.html#E1:28_1_2_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="radix_1.html#E4:28_1_2"><i><font color="Green" title="E21">X</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font>
<b>by </b><i><a class="txt" href="radix_1.html#E1:28_1_2_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="radix_1.html#D3" target="_self" title="RADIX_1:def.3">Def3</a>, <a class="txt" href="radix_1.html#E4:28_1_2"><i><font color="Green" title="E21">X</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:28_1_2_1"/>
<font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">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="E6:28_1_2"/>
<font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font>
 <b>by </b><i><a class="txt" href="radix_1.html#E3:28_1_2"><i><font color="Green" title="E20">A7</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/>


</div>
