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

<b>set </b><font color="Maroon">SDD</font> =  <a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font>;<br/>
<b>set </b><font color="Maroon">SDC</font> =  <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:39_1_1"/><i><font color="Green">E30</font></i>: 
 <a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">k</font> <a href="radix_1.html#K3" target="_self">-SD</a> 
 
<b>by </b><i><a class="txt" href="radix_1.html#E1:39"><i><font color="Green">E29</font></i></a>, </i>;<br/>
<a NAME="E2:39_1_1"/>
 <a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">k</font> <a href="radix_1.html#K3" target="_self">-SD</a> 
 
<b>by </b><i><a class="txt" href="radix_1.html#E1:39"><i><font color="Green">E29</font></i></a>, </i>;<br/>
<a NAME="E3:39_1_1"/><b>then </b><i><font color="Green">E37</font></i>: 
( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> &amp;  <a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2 )
 
<b>by </b><i><a class="txt" href="radix_1.html#E1:39"><i><font color="Green">E29</font></i></a>, <a class="txt" href="radix_1.html#E1:39_1_1"><i><font color="Green">E30</font></i></a>, </i>;<br/>
<a NAME="E4:39_1_1"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2">INT</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<a NAME="E5:39_1_1"/>
(  <a href="xcmplx_0.html#K4">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i/>;<br/>
<a NAME="E6:39_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" target="_self">Radix</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 )
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E7:39_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">k</font> <a href="radix_1.html#K3" target="_self">-SD</a> 
 
<b>by </b><i><a class="ref" href="radix_1.html#T3" target="_self">Th3</a></i>;<br/>
<b>hence </b><a NAME="E8:39_1_1"/>
<span class="p1">(<span class="default"><a href="radix_1.html#K12" target="_self">SD_Add_Data</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_1.html#K11" target="_self">SD_Add_Carry</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" target="_self">DigA</a> <font color="Maroon">y</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">k</font> <a href="radix_1.html#K3" target="_self">-SD</a> 
 ;<br/>


</div>
