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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:6"/><i><font color="Green">E7</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:6"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:6"/><b>then </b><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>hence </b> <a href="radix_3.html#K7">DigA_SDSub</a> <span class="p1">(<span class="default"><a href="radix_3.html#K10">SD2SDSub</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="radix_3.html#K9">SD2SDSubDigitS</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="radix_3.html#D8">RADIX_3:def 8</a></i>
<br/>.= 
 <a href="radix_3.html#K8">SD2SDSubDigit</a> <span class="p1">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="radix_4.html#E1:6"><i><font color="Green">E7</font></i></a>, <a class="txt" href="radix_4.html#E4:6"><i><font color="Green">E8</font></i></a>, <a class="ref" href="radix_3.html#D7">RADIX_3:def 7</a></i>
<br/>.= 
 <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="radix_3.html#D6">RADIX_3:def 6</a></i>
<br/>.= 
 <a href="radix_3.html#K5">SDSub_Add_Carry</a> <span class="p1">(<span class="default"><a href="radix_1.html#K4">DigA</a> <span class="p2">(<span class="default"><a href="radix_1.html#K10">DecSD</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/><br/>


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