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<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 <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="radix_3.html#K4" title="RADIX_3:func.4">-SD_Sub</a> </span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:32_1_2"/><i><font color="Green" title="E26">A4</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/> <a href="radix_3.html#K7" title="RADIX_3:func.7">DigA_SDSub</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_3.html#K9" title="RADIX_3:func.9">SD2SDSubDigitS</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">k</font>
 <b>and </b><br/><a NAME="E2:32_1_2"/><i><font color="Green" title="E27">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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> holds <br/> <a href="radix_3.html#K7" title="RADIX_3:func.7">DigA_SDSub</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_3.html#K9" title="RADIX_3:func.9">SD2SDSubDigitS</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">k</font>
 ;<br/>

<a NAME="E3:32_1_2"/><i><font color="Green" title="E28">A6</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="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &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="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_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>;<br/><b>assume </b><a NAME="E1:32_1_2_1"/><i><font color="Green" title="E29">A7</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#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</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_3.html#K7" title="RADIX_3:func.7">DigA_SDSub</a> <font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c6">j</font>
<b>by </b><i><a class="ref" href="radix_3.html#D5" target="_self" title="RADIX_3:def.5">Def5</a></i>
<br/>.= 
 <a href="radix_3.html#K9" title="RADIX_3:func.9">SD2SDSubDigitS</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c2">k</font>
<b>by </b><i><a class="txt" href="radix_3.html#E1:32_1_2"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="radix_3.html#E1:32_1_2_1"><i><font color="Green" title="E29">A7</font></i></a></i>
<br/>.= 
 <a href="radix_3.html#K7" title="RADIX_3:func.7">DigA_SDSub</a> <font color="Maroon" title="c5">k2</font>,<font color="Maroon" title="c6">j</font>
<b>by </b><i><a class="txt" href="radix_3.html#E2:32_1_2"><i><font color="Green" title="E27">A5</font></i></a>, <a class="txt" href="radix_3.html#E1:32_1_2_1"><i><font color="Green" title="E29">A7</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_3.html#E1:32_1_2_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="radix_3.html#D5" target="_self" title="RADIX_3:def.5">Def5</a></i>
;<br/><b>hence </b><a NAME="E3:32_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>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:32_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_3.html#E3:32_1_2"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


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