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<b>let </b><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E7">A1</font></i>: 
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font>
 ;<br/>

<a NAME="E2:6"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:6"/><b>then </b><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<b>hence </b> <a href="radix_3.html#K7" title="RADIX_3:func.7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10" title="RADIX_3:func.10">SD2SDSub</a> <span class="p2">(<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="c3">n</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="radix_3.html#K9" title="RADIX_3:func.9">SD2SDSubDigitS</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="c3">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="ref" href="radix_3.html#D8" title="RADIX_3:def.8">RADIX_3:def 8</a></i>
<br/>.= 
 <a href="radix_3.html#K8" title="RADIX_3:func.8">SD2SDSubDigit</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="c3">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:6"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="radix_4.html#E4:6"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="radix_3.html#D7" title="RADIX_3:def.7">RADIX_3:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p2">(<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="c3">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="ref" href="radix_3.html#D6" title="RADIX_3:def.6">RADIX_3:def 6</a></i>
<br/>.= 
 <a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> <span class="p2">(<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="c3">n</font>,<font color="Maroon" title="c1">k</font></span>)</span>,<font color="Maroon" title="c3">n</font></span>)</span>,<font color="Maroon" title="c1">k</font>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
;<br/><br/>


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