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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">i2</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>





<b>assume </b><a NAME="E1:26"/><i><font color="Green">E30</font></i>: 
( 2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">k</font> <a href="radix_1.html#K3">-SD</a>  &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">k</font> <a href="radix_1.html#K3">-SD</a>  )
 ;<br/>

<a NAME="E2:26"/><b>then </b><i><font color="Green">E35</font></i>: 
(  <a href="radix_3.html#K6" target="_self">SDSub_Add_Data</a> <font color="Maroon">i1</font>,<font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="radix_1.html#K1">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> &amp;  <a href="radix_3.html#K6" target="_self">SDSub_Add_Data</a> <font color="Maroon">i1</font>,<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">Radix</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 
<b>by </b><i/>;<br/>
<a NAME="E3:26"/><i><font color="Green">E37</font></i>: 
(  <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">i2</font>,<font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> 1 &amp;  <a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">i2</font>,<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:26"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="radix_3.html#K6" target="_self">SDSub_Add_Data</a> <font color="Maroon">i1</font>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">i2</font>,<font color="Maroon">k</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <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">Radix</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></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>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E5:26"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="radix_3.html#K6" target="_self">SDSub_Add_Data</a> <font color="Maroon">i1</font>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">i2</font>,<font color="Maroon">k</font></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">Radix</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</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="E6:26"/><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><a href="radix_3.html#K6" target="_self">SDSub_Add_Data</a> <font color="Maroon">i1</font>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">i2</font>,<font color="Maroon">k</font></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/>
<b>thus </b><a NAME="E7:26"/>
<span class="p1">(<span class="default"><a href="radix_3.html#K6" target="_self">SDSub_Add_Data</a> <font color="Maroon">i1</font>,<font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="radix_3.html#K5" target="_self">SDSub_Add_Carry</a> <font color="Maroon">i2</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">k</font> <a href="radix_3.html#K4" target="_self">-SD_Sub</a> 
 <b>by </b><i>, , </i>;<br/>


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